Ical
https://mathematics.huji.ac.il/calendar?type=month&month=term
en<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows?delta=0" >Kazhdan Sunday seminar: Elon Lindenstrauss "Arithmetic applications of diagonal flows" </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows
Elon Lindenstrauss "Arithmetic applications of diagonal flows"
I will give an introduction to the dynamics of higher rank diagonal flows on homogeneous spaces,
including both the rigidity theorems of such flows and their applications to orbits of arithmetic interest,
in particular CM points and integer points on spheres.
I hope to cover parts of the following papers:
Einsiedler, Manfred ; Lindenstrauss, Elon ; Michel, Philippe ; Venkatesh, Akshay . The distribution of closed geodesics
on the modular surface, and Duke's theorem. Enseign. Math. (2) 58 (2012), no. 3-4, 249--313.
Einsiedler, M., Lindenstrauss, E., Symmetry of entropy in higher rank diagonalizable actions and measure classification.
arXiv e-prints arXiv:1803.07762.
Einsiedler, M. & Lindenstrauss, E. .Joinings of higher rank torus actions on homogeneous spaces. Publ.math.IHES (2019).
<a href="https://doi.org/10.1007/s10240-019-00103-y">https://doi.org/10.1007/s10240-019-00103-y</a>
Khayutin, Ilya . Joint equidistribution of CM points. Ann. of Math. (2) 189 (2019), no. 1, 145--276.
Aka, Menny ; Einsiedler, Manfred ; Shapira, Uri . Integer points on spheres and their orthogonal lattices.
Invent. Math. 206 (2016), no. 2, 379--396.Sun, 27 Oct 2019 09:00:00 +0000Anonymous92997 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil?delta=0" >Kazhdan Sunday seminar: "Computation, quantumness, symplectic geometry, and information" (Gil Kalai, Leonid Polterovich, with participation of Dorit Aharonov and Guy Kindler)</a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil
Tentative syllabus
1. Mathematical models of classical and quantum mechanics.
2. Correspondence principle and quantization.
3. Classical and quantum computation: gates, circuits, algorithms
(Shor, Grover). Solovay-Kitaev. Some ideas of cryptography
4. Quantum noise and measurement, and rigidity of the Poisson bracket.
5. Noisy classical and quantum computing and error correction, threshold theorem- quantum fault tolerance (small noise is good for quantum computation). Kitaev's surface code.
6. Quantum speed limit/time-energy uncertainty vs symplectic displacement energy.
7. Time-energy uncertainty and quantum computation (Dorit or her student?)
8. Berezin transform, Markov chains, spectral gap, noise.
9. Adiabatic computation, quantum PCP (probabilistically checkable proofs) conjecture
[? under discussion]
10. Noise stability and noise sensitivity of Boolean functions, noisy boson
sampling
11. Connection to quantum field theory (Guy?).
Literature:
Aharonov, D. Quantum computation, In "Annual Reviews of Computational Physics" VI, 1999
(pp. 259-346).
<a href="https://arxiv.org/abs/quant-ph/9812037">https://arxiv.org/abs/quant-ph/9812037</a>
Kalai, G., Three puzzles on mathematics computations, and games, Proc. Int
Congress Math 2018, Rio de Janeiro, Vol. 1 pp. 551–606.
<a href="https://arxiv.org/abs/1801.02602">https://arxiv.org/abs/1801.02602</a>
Nielsen, M.A., and Chuang, I.L., Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000.
Polterovich, L., Symplectic rigidity and quantum mechanics, European Congress of Mathematics, 155–179, Eur. Math. Soc., Zürich, 2018.
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rigidity-and-quantum-mechanics">https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rig...</a>
Polterovich L., and Rosen D., Function theory on symplectic manifolds. American Mathematical Society; 2014. [Chapters 1,9]
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/function-theory-on-symplectic-manifolds">https://sites.google.com/site/polterov/miscellaneoustexts/function-theor...</a>
Wigderson, A., Mathematics and computation, Princeton Univ. Press, 2019.
<a href="https://www.math.ias.edu/files/mathandcomp.pdf">https://www.math.ias.edu/files/mathandcomp.pdf</a>Sun, 27 Oct 2019 12:00:00 +0000Anonymous92999 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze?delta=0" >Kazhdan Sunday seminar: Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze) </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze
Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze)
Abstract: We shall discuss (Weil) cohomology theories for algebraic varieties.
When working with schemes over p-complete rings and taking cohomologies with p-complete coefficients one gets a plurality of such cohomology theories (e'tale, De-Rahm, Crystalline, etc.. ). The comparison between these different cohomology theories is a subtle subject known as "p-adic hodge theory" .
Recently Bhatt and Scholze defined a new such cohomology theory called prismatic cohomology. Remarkably, prismatic cohomology is easier to define than most p-adic cohomology theories and in the same specialized to each of them.The main new tool is the notions of delta-rings and prisms.
We shall start discussing general Weil) cohomology theories for algebraic varieties and give basic examples, we then move to develop the algebra of delta-rings and prisms, we then define the prisamtic site and prismatic cohomology. We shall then continue with comparison theorems and finally some applications Sun, 27 Oct 2019 14:00:00 +0000Anonymous92998 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/hagai-lavner-huji?delta=0" >Hagai Lavner (HUJI)</a>
https://mathematics.huji.ac.il/event/hagai-lavner-huji
Tue, 29 Oct 2019 10:00:00 +0000Anonymous93510 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows?delta=1" >Kazhdan Sunday seminar: Elon Lindenstrauss "Arithmetic applications of diagonal flows" </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows
Elon Lindenstrauss "Arithmetic applications of diagonal flows"
I will give an introduction to the dynamics of higher rank diagonal flows on homogeneous spaces,
including both the rigidity theorems of such flows and their applications to orbits of arithmetic interest,
in particular CM points and integer points on spheres.
I hope to cover parts of the following papers:
Einsiedler, Manfred ; Lindenstrauss, Elon ; Michel, Philippe ; Venkatesh, Akshay . The distribution of closed geodesics
on the modular surface, and Duke's theorem. Enseign. Math. (2) 58 (2012), no. 3-4, 249--313.
Einsiedler, M., Lindenstrauss, E., Symmetry of entropy in higher rank diagonalizable actions and measure classification.
arXiv e-prints arXiv:1803.07762.
Einsiedler, M. & Lindenstrauss, E. .Joinings of higher rank torus actions on homogeneous spaces. Publ.math.IHES (2019).
<a href="https://doi.org/10.1007/s10240-019-00103-y">https://doi.org/10.1007/s10240-019-00103-y</a>
Khayutin, Ilya . Joint equidistribution of CM points. Ann. of Math. (2) 189 (2019), no. 1, 145--276.
Aka, Menny ; Einsiedler, Manfred ; Shapira, Uri . Integer points on spheres and their orthogonal lattices.
Invent. Math. 206 (2016), no. 2, 379--396.Sun, 27 Oct 2019 09:00:00 +0000Anonymous92997 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil?delta=1" >Kazhdan Sunday seminar: "Computation, quantumness, symplectic geometry, and information" (Gil Kalai, Leonid Polterovich, with participation of Dorit Aharonov and Guy Kindler)</a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil
Tentative syllabus
1. Mathematical models of classical and quantum mechanics.
2. Correspondence principle and quantization.
3. Classical and quantum computation: gates, circuits, algorithms
(Shor, Grover). Solovay-Kitaev. Some ideas of cryptography
4. Quantum noise and measurement, and rigidity of the Poisson bracket.
5. Noisy classical and quantum computing and error correction, threshold theorem- quantum fault tolerance (small noise is good for quantum computation). Kitaev's surface code.
6. Quantum speed limit/time-energy uncertainty vs symplectic displacement energy.
7. Time-energy uncertainty and quantum computation (Dorit or her student?)
8. Berezin transform, Markov chains, spectral gap, noise.
9. Adiabatic computation, quantum PCP (probabilistically checkable proofs) conjecture
[? under discussion]
10. Noise stability and noise sensitivity of Boolean functions, noisy boson
sampling
11. Connection to quantum field theory (Guy?).
Literature:
Aharonov, D. Quantum computation, In "Annual Reviews of Computational Physics" VI, 1999
(pp. 259-346).
<a href="https://arxiv.org/abs/quant-ph/9812037">https://arxiv.org/abs/quant-ph/9812037</a>
Kalai, G., Three puzzles on mathematics computations, and games, Proc. Int
Congress Math 2018, Rio de Janeiro, Vol. 1 pp. 551–606.
<a href="https://arxiv.org/abs/1801.02602">https://arxiv.org/abs/1801.02602</a>
Nielsen, M.A., and Chuang, I.L., Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000.
Polterovich, L., Symplectic rigidity and quantum mechanics, European Congress of Mathematics, 155–179, Eur. Math. Soc., Zürich, 2018.
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rigidity-and-quantum-mechanics">https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rig...</a>
Polterovich L., and Rosen D., Function theory on symplectic manifolds. American Mathematical Society; 2014. [Chapters 1,9]
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/function-theory-on-symplectic-manifolds">https://sites.google.com/site/polterov/miscellaneoustexts/function-theor...</a>
Wigderson, A., Mathematics and computation, Princeton Univ. Press, 2019.
<a href="https://www.math.ias.edu/files/mathandcomp.pdf">https://www.math.ias.edu/files/mathandcomp.pdf</a>Sun, 27 Oct 2019 12:00:00 +0000Anonymous92999 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze?delta=1" >Kazhdan Sunday seminar: Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze) </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze
Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze)
Abstract: We shall discuss (Weil) cohomology theories for algebraic varieties.
When working with schemes over p-complete rings and taking cohomologies with p-complete coefficients one gets a plurality of such cohomology theories (e'tale, De-Rahm, Crystalline, etc.. ). The comparison between these different cohomology theories is a subtle subject known as "p-adic hodge theory" .
Recently Bhatt and Scholze defined a new such cohomology theory called prismatic cohomology. Remarkably, prismatic cohomology is easier to define than most p-adic cohomology theories and in the same specialized to each of them.The main new tool is the notions of delta-rings and prisms.
We shall start discussing general Weil) cohomology theories for algebraic varieties and give basic examples, we then move to develop the algebra of delta-rings and prisms, we then define the prisamtic site and prismatic cohomology. We shall then continue with comparison theorems and finally some applications Sun, 27 Oct 2019 14:00:00 +0000Anonymous92998 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/or-landesberg?delta=0" >Or Landesberg</a>
https://mathematics.huji.ac.il/event/or-landesberg
Tue, 05 Nov 2019 12:00:00 +0000Anonymous93424 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/analysis-seminar-eyal-seelig-huji-tba?delta=0" >Analysis Seminar: Eyal Seelig (HUJI) "TBA"</a>
https://mathematics.huji.ac.il/event/analysis-seminar-eyal-seelig-huji-tba
Wed, 06 Nov 2019 10:00:00 +0000Anonymous93507 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows?delta=2" >Kazhdan Sunday seminar: Elon Lindenstrauss "Arithmetic applications of diagonal flows" </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows
Elon Lindenstrauss "Arithmetic applications of diagonal flows"
I will give an introduction to the dynamics of higher rank diagonal flows on homogeneous spaces,
including both the rigidity theorems of such flows and their applications to orbits of arithmetic interest,
in particular CM points and integer points on spheres.
I hope to cover parts of the following papers:
Einsiedler, Manfred ; Lindenstrauss, Elon ; Michel, Philippe ; Venkatesh, Akshay . The distribution of closed geodesics
on the modular surface, and Duke's theorem. Enseign. Math. (2) 58 (2012), no. 3-4, 249--313.
Einsiedler, M., Lindenstrauss, E., Symmetry of entropy in higher rank diagonalizable actions and measure classification.
arXiv e-prints arXiv:1803.07762.
Einsiedler, M. & Lindenstrauss, E. .Joinings of higher rank torus actions on homogeneous spaces. Publ.math.IHES (2019).
<a href="https://doi.org/10.1007/s10240-019-00103-y">https://doi.org/10.1007/s10240-019-00103-y</a>
Khayutin, Ilya . Joint equidistribution of CM points. Ann. of Math. (2) 189 (2019), no. 1, 145--276.
Aka, Menny ; Einsiedler, Manfred ; Shapira, Uri . Integer points on spheres and their orthogonal lattices.
Invent. Math. 206 (2016), no. 2, 379--396.Sun, 27 Oct 2019 09:00:00 +0000Anonymous92997 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil?delta=2" >Kazhdan Sunday seminar: "Computation, quantumness, symplectic geometry, and information" (Gil Kalai, Leonid Polterovich, with participation of Dorit Aharonov and Guy Kindler)</a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil
Tentative syllabus
1. Mathematical models of classical and quantum mechanics.
2. Correspondence principle and quantization.
3. Classical and quantum computation: gates, circuits, algorithms
(Shor, Grover). Solovay-Kitaev. Some ideas of cryptography
4. Quantum noise and measurement, and rigidity of the Poisson bracket.
5. Noisy classical and quantum computing and error correction, threshold theorem- quantum fault tolerance (small noise is good for quantum computation). Kitaev's surface code.
6. Quantum speed limit/time-energy uncertainty vs symplectic displacement energy.
7. Time-energy uncertainty and quantum computation (Dorit or her student?)
8. Berezin transform, Markov chains, spectral gap, noise.
9. Adiabatic computation, quantum PCP (probabilistically checkable proofs) conjecture
[? under discussion]
10. Noise stability and noise sensitivity of Boolean functions, noisy boson
sampling
11. Connection to quantum field theory (Guy?).
Literature:
Aharonov, D. Quantum computation, In "Annual Reviews of Computational Physics" VI, 1999
(pp. 259-346).
<a href="https://arxiv.org/abs/quant-ph/9812037">https://arxiv.org/abs/quant-ph/9812037</a>
Kalai, G., Three puzzles on mathematics computations, and games, Proc. Int
Congress Math 2018, Rio de Janeiro, Vol. 1 pp. 551–606.
<a href="https://arxiv.org/abs/1801.02602">https://arxiv.org/abs/1801.02602</a>
Nielsen, M.A., and Chuang, I.L., Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000.
Polterovich, L., Symplectic rigidity and quantum mechanics, European Congress of Mathematics, 155–179, Eur. Math. Soc., Zürich, 2018.
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rigidity-and-quantum-mechanics">https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rig...</a>
Polterovich L., and Rosen D., Function theory on symplectic manifolds. American Mathematical Society; 2014. [Chapters 1,9]
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/function-theory-on-symplectic-manifolds">https://sites.google.com/site/polterov/miscellaneoustexts/function-theor...</a>
Wigderson, A., Mathematics and computation, Princeton Univ. Press, 2019.
<a href="https://www.math.ias.edu/files/mathandcomp.pdf">https://www.math.ias.edu/files/mathandcomp.pdf</a>Sun, 27 Oct 2019 12:00:00 +0000Anonymous92999 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze?delta=2" >Kazhdan Sunday seminar: Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze) </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze
Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze)
Abstract: We shall discuss (Weil) cohomology theories for algebraic varieties.
When working with schemes over p-complete rings and taking cohomologies with p-complete coefficients one gets a plurality of such cohomology theories (e'tale, De-Rahm, Crystalline, etc.. ). The comparison between these different cohomology theories is a subtle subject known as "p-adic hodge theory" .
Recently Bhatt and Scholze defined a new such cohomology theory called prismatic cohomology. Remarkably, prismatic cohomology is easier to define than most p-adic cohomology theories and in the same specialized to each of them.The main new tool is the notions of delta-rings and prisms.
We shall start discussing general Weil) cohomology theories for algebraic varieties and give basic examples, we then move to develop the algebra of delta-rings and prisms, we then define the prisamtic site and prismatic cohomology. We shall then continue with comparison theorems and finally some applications Sun, 27 Oct 2019 14:00:00 +0000Anonymous92998 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/uri-gabor?delta=0" >Uri Gabor</a>
https://mathematics.huji.ac.il/event/uri-gabor
Tue, 12 Nov 2019 12:00:00 +0000Anonymous93726 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/analysis-seminar-misha-sodin-tau-tba?delta=0" >Analysis Seminar: Misha Sodin (TAU) "TBA"</a>
https://mathematics.huji.ac.il/event/analysis-seminar-misha-sodin-tau-tba
Wed, 13 Nov 2019 10:00:00 +0000Anonymous92819 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows?delta=3" >Kazhdan Sunday seminar: Elon Lindenstrauss "Arithmetic applications of diagonal flows" </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows
Elon Lindenstrauss "Arithmetic applications of diagonal flows"
I will give an introduction to the dynamics of higher rank diagonal flows on homogeneous spaces,
including both the rigidity theorems of such flows and their applications to orbits of arithmetic interest,
in particular CM points and integer points on spheres.
I hope to cover parts of the following papers:
Einsiedler, Manfred ; Lindenstrauss, Elon ; Michel, Philippe ; Venkatesh, Akshay . The distribution of closed geodesics
on the modular surface, and Duke's theorem. Enseign. Math. (2) 58 (2012), no. 3-4, 249--313.
Einsiedler, M., Lindenstrauss, E., Symmetry of entropy in higher rank diagonalizable actions and measure classification.
arXiv e-prints arXiv:1803.07762.
Einsiedler, M. & Lindenstrauss, E. .Joinings of higher rank torus actions on homogeneous spaces. Publ.math.IHES (2019).
<a href="https://doi.org/10.1007/s10240-019-00103-y">https://doi.org/10.1007/s10240-019-00103-y</a>
Khayutin, Ilya . Joint equidistribution of CM points. Ann. of Math. (2) 189 (2019), no. 1, 145--276.
Aka, Menny ; Einsiedler, Manfred ; Shapira, Uri . Integer points on spheres and their orthogonal lattices.
Invent. Math. 206 (2016), no. 2, 379--396.Sun, 27 Oct 2019 09:00:00 +0000Anonymous92997 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil?delta=3" >Kazhdan Sunday seminar: "Computation, quantumness, symplectic geometry, and information" (Gil Kalai, Leonid Polterovich, with participation of Dorit Aharonov and Guy Kindler)</a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil
Tentative syllabus
1. Mathematical models of classical and quantum mechanics.
2. Correspondence principle and quantization.
3. Classical and quantum computation: gates, circuits, algorithms
(Shor, Grover). Solovay-Kitaev. Some ideas of cryptography
4. Quantum noise and measurement, and rigidity of the Poisson bracket.
5. Noisy classical and quantum computing and error correction, threshold theorem- quantum fault tolerance (small noise is good for quantum computation). Kitaev's surface code.
6. Quantum speed limit/time-energy uncertainty vs symplectic displacement energy.
7. Time-energy uncertainty and quantum computation (Dorit or her student?)
8. Berezin transform, Markov chains, spectral gap, noise.
9. Adiabatic computation, quantum PCP (probabilistically checkable proofs) conjecture
[? under discussion]
10. Noise stability and noise sensitivity of Boolean functions, noisy boson
sampling
11. Connection to quantum field theory (Guy?).
Literature:
Aharonov, D. Quantum computation, In "Annual Reviews of Computational Physics" VI, 1999
(pp. 259-346).
<a href="https://arxiv.org/abs/quant-ph/9812037">https://arxiv.org/abs/quant-ph/9812037</a>
Kalai, G., Three puzzles on mathematics computations, and games, Proc. Int
Congress Math 2018, Rio de Janeiro, Vol. 1 pp. 551–606.
<a href="https://arxiv.org/abs/1801.02602">https://arxiv.org/abs/1801.02602</a>
Nielsen, M.A., and Chuang, I.L., Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000.
Polterovich, L., Symplectic rigidity and quantum mechanics, European Congress of Mathematics, 155–179, Eur. Math. Soc., Zürich, 2018.
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rigidity-and-quantum-mechanics">https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rig...</a>
Polterovich L., and Rosen D., Function theory on symplectic manifolds. American Mathematical Society; 2014. [Chapters 1,9]
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/function-theory-on-symplectic-manifolds">https://sites.google.com/site/polterov/miscellaneoustexts/function-theor...</a>
Wigderson, A., Mathematics and computation, Princeton Univ. Press, 2019.
<a href="https://www.math.ias.edu/files/mathandcomp.pdf">https://www.math.ias.edu/files/mathandcomp.pdf</a>Sun, 27 Oct 2019 12:00:00 +0000Anonymous92999 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze?delta=3" >Kazhdan Sunday seminar: Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze) </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze
Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze)
Abstract: We shall discuss (Weil) cohomology theories for algebraic varieties.
When working with schemes over p-complete rings and taking cohomologies with p-complete coefficients one gets a plurality of such cohomology theories (e'tale, De-Rahm, Crystalline, etc.. ). The comparison between these different cohomology theories is a subtle subject known as "p-adic hodge theory" .
Recently Bhatt and Scholze defined a new such cohomology theory called prismatic cohomology. Remarkably, prismatic cohomology is easier to define than most p-adic cohomology theories and in the same specialized to each of them.The main new tool is the notions of delta-rings and prisms.
We shall start discussing general Weil) cohomology theories for algebraic varieties and give basic examples, we then move to develop the algebra of delta-rings and prisms, we then define the prisamtic site and prismatic cohomology. We shall then continue with comparison theorems and finally some applications Sun, 27 Oct 2019 14:00:00 +0000Anonymous92998 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/analysis-seminar-genadi-levin-tba?delta=0" >Analysis Seminar: Genadi Levin "TBA"</a>
https://mathematics.huji.ac.il/event/analysis-seminar-genadi-levin-tba
Wed, 20 Nov 2019 10:00:00 +0000Anonymous92349 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows?delta=4" >Kazhdan Sunday seminar: Elon Lindenstrauss "Arithmetic applications of diagonal flows" </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows
Elon Lindenstrauss "Arithmetic applications of diagonal flows"
I will give an introduction to the dynamics of higher rank diagonal flows on homogeneous spaces,
including both the rigidity theorems of such flows and their applications to orbits of arithmetic interest,
in particular CM points and integer points on spheres.
I hope to cover parts of the following papers:
Einsiedler, Manfred ; Lindenstrauss, Elon ; Michel, Philippe ; Venkatesh, Akshay . The distribution of closed geodesics
on the modular surface, and Duke's theorem. Enseign. Math. (2) 58 (2012), no. 3-4, 249--313.
Einsiedler, M., Lindenstrauss, E., Symmetry of entropy in higher rank diagonalizable actions and measure classification.
arXiv e-prints arXiv:1803.07762.
Einsiedler, M. & Lindenstrauss, E. .Joinings of higher rank torus actions on homogeneous spaces. Publ.math.IHES (2019).
<a href="https://doi.org/10.1007/s10240-019-00103-y">https://doi.org/10.1007/s10240-019-00103-y</a>
Khayutin, Ilya . Joint equidistribution of CM points. Ann. of Math. (2) 189 (2019), no. 1, 145--276.
Aka, Menny ; Einsiedler, Manfred ; Shapira, Uri . Integer points on spheres and their orthogonal lattices.
Invent. Math. 206 (2016), no. 2, 379--396.Sun, 27 Oct 2019 09:00:00 +0000Anonymous92997 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil?delta=4" >Kazhdan Sunday seminar: "Computation, quantumness, symplectic geometry, and information" (Gil Kalai, Leonid Polterovich, with participation of Dorit Aharonov and Guy Kindler)</a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil
Tentative syllabus
1. Mathematical models of classical and quantum mechanics.
2. Correspondence principle and quantization.
3. Classical and quantum computation: gates, circuits, algorithms
(Shor, Grover). Solovay-Kitaev. Some ideas of cryptography
4. Quantum noise and measurement, and rigidity of the Poisson bracket.
5. Noisy classical and quantum computing and error correction, threshold theorem- quantum fault tolerance (small noise is good for quantum computation). Kitaev's surface code.
6. Quantum speed limit/time-energy uncertainty vs symplectic displacement energy.
7. Time-energy uncertainty and quantum computation (Dorit or her student?)
8. Berezin transform, Markov chains, spectral gap, noise.
9. Adiabatic computation, quantum PCP (probabilistically checkable proofs) conjecture
[? under discussion]
10. Noise stability and noise sensitivity of Boolean functions, noisy boson
sampling
11. Connection to quantum field theory (Guy?).
Literature:
Aharonov, D. Quantum computation, In "Annual Reviews of Computational Physics" VI, 1999
(pp. 259-346).
<a href="https://arxiv.org/abs/quant-ph/9812037">https://arxiv.org/abs/quant-ph/9812037</a>
Kalai, G., Three puzzles on mathematics computations, and games, Proc. Int
Congress Math 2018, Rio de Janeiro, Vol. 1 pp. 551–606.
<a href="https://arxiv.org/abs/1801.02602">https://arxiv.org/abs/1801.02602</a>
Nielsen, M.A., and Chuang, I.L., Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000.
Polterovich, L., Symplectic rigidity and quantum mechanics, European Congress of Mathematics, 155–179, Eur. Math. Soc., Zürich, 2018.
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rigidity-and-quantum-mechanics">https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rig...</a>
Polterovich L., and Rosen D., Function theory on symplectic manifolds. American Mathematical Society; 2014. [Chapters 1,9]
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/function-theory-on-symplectic-manifolds">https://sites.google.com/site/polterov/miscellaneoustexts/function-theor...</a>
Wigderson, A., Mathematics and computation, Princeton Univ. Press, 2019.
<a href="https://www.math.ias.edu/files/mathandcomp.pdf">https://www.math.ias.edu/files/mathandcomp.pdf</a>Sun, 27 Oct 2019 12:00:00 +0000Anonymous92999 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze?delta=4" >Kazhdan Sunday seminar: Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze) </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze
Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze)
Abstract: We shall discuss (Weil) cohomology theories for algebraic varieties.
When working with schemes over p-complete rings and taking cohomologies with p-complete coefficients one gets a plurality of such cohomology theories (e'tale, De-Rahm, Crystalline, etc.. ). The comparison between these different cohomology theories is a subtle subject known as "p-adic hodge theory" .
Recently Bhatt and Scholze defined a new such cohomology theory called prismatic cohomology. Remarkably, prismatic cohomology is easier to define than most p-adic cohomology theories and in the same specialized to each of them.The main new tool is the notions of delta-rings and prisms.
We shall start discussing general Weil) cohomology theories for algebraic varieties and give basic examples, we then move to develop the algebra of delta-rings and prisms, we then define the prisamtic site and prismatic cohomology. We shall then continue with comparison theorems and finally some applications Sun, 27 Oct 2019 14:00:00 +0000Anonymous92998 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/analysis-serminar-ami-viselter-haifa-tba?delta=0" >Analysis Serminar: Ami Viselter, Haifa "TBA"</a>
https://mathematics.huji.ac.il/event/analysis-serminar-ami-viselter-haifa-tba
Wed, 27 Nov 2019 10:00:00 +0000Anonymous92350 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows?delta=5" >Kazhdan Sunday seminar: Elon Lindenstrauss "Arithmetic applications of diagonal flows" </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows
Elon Lindenstrauss "Arithmetic applications of diagonal flows"
I will give an introduction to the dynamics of higher rank diagonal flows on homogeneous spaces,
including both the rigidity theorems of such flows and their applications to orbits of arithmetic interest,
in particular CM points and integer points on spheres.
I hope to cover parts of the following papers:
Einsiedler, Manfred ; Lindenstrauss, Elon ; Michel, Philippe ; Venkatesh, Akshay . The distribution of closed geodesics
on the modular surface, and Duke's theorem. Enseign. Math. (2) 58 (2012), no. 3-4, 249--313.
Einsiedler, M., Lindenstrauss, E., Symmetry of entropy in higher rank diagonalizable actions and measure classification.
arXiv e-prints arXiv:1803.07762.
Einsiedler, M. & Lindenstrauss, E. .Joinings of higher rank torus actions on homogeneous spaces. Publ.math.IHES (2019).
<a href="https://doi.org/10.1007/s10240-019-00103-y">https://doi.org/10.1007/s10240-019-00103-y</a>
Khayutin, Ilya . Joint equidistribution of CM points. Ann. of Math. (2) 189 (2019), no. 1, 145--276.
Aka, Menny ; Einsiedler, Manfred ; Shapira, Uri . Integer points on spheres and their orthogonal lattices.
Invent. Math. 206 (2016), no. 2, 379--396.Sun, 27 Oct 2019 09:00:00 +0000Anonymous92997 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil?delta=5" >Kazhdan Sunday seminar: "Computation, quantumness, symplectic geometry, and information" (Gil Kalai, Leonid Polterovich, with participation of Dorit Aharonov and Guy Kindler)</a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil
Tentative syllabus
1. Mathematical models of classical and quantum mechanics.
2. Correspondence principle and quantization.
3. Classical and quantum computation: gates, circuits, algorithms
(Shor, Grover). Solovay-Kitaev. Some ideas of cryptography
4. Quantum noise and measurement, and rigidity of the Poisson bracket.
5. Noisy classical and quantum computing and error correction, threshold theorem- quantum fault tolerance (small noise is good for quantum computation). Kitaev's surface code.
6. Quantum speed limit/time-energy uncertainty vs symplectic displacement energy.
7. Time-energy uncertainty and quantum computation (Dorit or her student?)
8. Berezin transform, Markov chains, spectral gap, noise.
9. Adiabatic computation, quantum PCP (probabilistically checkable proofs) conjecture
[? under discussion]
10. Noise stability and noise sensitivity of Boolean functions, noisy boson
sampling
11. Connection to quantum field theory (Guy?).
Literature:
Aharonov, D. Quantum computation, In "Annual Reviews of Computational Physics" VI, 1999
(pp. 259-346).
<a href="https://arxiv.org/abs/quant-ph/9812037">https://arxiv.org/abs/quant-ph/9812037</a>
Kalai, G., Three puzzles on mathematics computations, and games, Proc. Int
Congress Math 2018, Rio de Janeiro, Vol. 1 pp. 551–606.
<a href="https://arxiv.org/abs/1801.02602">https://arxiv.org/abs/1801.02602</a>
Nielsen, M.A., and Chuang, I.L., Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000.
Polterovich, L., Symplectic rigidity and quantum mechanics, European Congress of Mathematics, 155–179, Eur. Math. Soc., Zürich, 2018.
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rigidity-and-quantum-mechanics">https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rig...</a>
Polterovich L., and Rosen D., Function theory on symplectic manifolds. American Mathematical Society; 2014. [Chapters 1,9]
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/function-theory-on-symplectic-manifolds">https://sites.google.com/site/polterov/miscellaneoustexts/function-theor...</a>
Wigderson, A., Mathematics and computation, Princeton Univ. Press, 2019.
<a href="https://www.math.ias.edu/files/mathandcomp.pdf">https://www.math.ias.edu/files/mathandcomp.pdf</a>Sun, 27 Oct 2019 12:00:00 +0000Anonymous92999 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze?delta=5" >Kazhdan Sunday seminar: Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze) </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze
Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze)
Abstract: We shall discuss (Weil) cohomology theories for algebraic varieties.
When working with schemes over p-complete rings and taking cohomologies with p-complete coefficients one gets a plurality of such cohomology theories (e'tale, De-Rahm, Crystalline, etc.. ). The comparison between these different cohomology theories is a subtle subject known as "p-adic hodge theory" .
Recently Bhatt and Scholze defined a new such cohomology theory called prismatic cohomology. Remarkably, prismatic cohomology is easier to define than most p-adic cohomology theories and in the same specialized to each of them.The main new tool is the notions of delta-rings and prisms.
We shall start discussing general Weil) cohomology theories for algebraic varieties and give basic examples, we then move to develop the algebra of delta-rings and prisms, we then define the prisamtic site and prismatic cohomology. We shall then continue with comparison theorems and finally some applications Sun, 27 Oct 2019 14:00:00 +0000Anonymous92998 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/uri-gabor-0?delta=0" >Uri Gabor</a>
https://mathematics.huji.ac.il/event/uri-gabor-0
Tue, 03 Dec 2019 10:00:00 +0000Anonymous93728 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/analysis-seminar-orr-shalit-technion-tba?delta=0" >Analysis Seminar: Orr Shalit (Technion) "TBA"</a>
https://mathematics.huji.ac.il/event/analysis-seminar-orr-shalit-technion-tba
Wed, 04 Dec 2019 10:00:00 +0000Anonymous92352 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows?delta=6" >Kazhdan Sunday seminar: Elon Lindenstrauss "Arithmetic applications of diagonal flows" </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows
Elon Lindenstrauss "Arithmetic applications of diagonal flows"
I will give an introduction to the dynamics of higher rank diagonal flows on homogeneous spaces,
including both the rigidity theorems of such flows and their applications to orbits of arithmetic interest,
in particular CM points and integer points on spheres.
I hope to cover parts of the following papers:
Einsiedler, Manfred ; Lindenstrauss, Elon ; Michel, Philippe ; Venkatesh, Akshay . The distribution of closed geodesics
on the modular surface, and Duke's theorem. Enseign. Math. (2) 58 (2012), no. 3-4, 249--313.
Einsiedler, M., Lindenstrauss, E., Symmetry of entropy in higher rank diagonalizable actions and measure classification.
arXiv e-prints arXiv:1803.07762.
Einsiedler, M. & Lindenstrauss, E. .Joinings of higher rank torus actions on homogeneous spaces. Publ.math.IHES (2019).
<a href="https://doi.org/10.1007/s10240-019-00103-y">https://doi.org/10.1007/s10240-019-00103-y</a>
Khayutin, Ilya . Joint equidistribution of CM points. Ann. of Math. (2) 189 (2019), no. 1, 145--276.
Aka, Menny ; Einsiedler, Manfred ; Shapira, Uri . Integer points on spheres and their orthogonal lattices.
Invent. Math. 206 (2016), no. 2, 379--396.Sun, 27 Oct 2019 09:00:00 +0000Anonymous92997 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil?delta=6" >Kazhdan Sunday seminar: "Computation, quantumness, symplectic geometry, and information" (Gil Kalai, Leonid Polterovich, with participation of Dorit Aharonov and Guy Kindler)</a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil
Tentative syllabus
1. Mathematical models of classical and quantum mechanics.
2. Correspondence principle and quantization.
3. Classical and quantum computation: gates, circuits, algorithms
(Shor, Grover). Solovay-Kitaev. Some ideas of cryptography
4. Quantum noise and measurement, and rigidity of the Poisson bracket.
5. Noisy classical and quantum computing and error correction, threshold theorem- quantum fault tolerance (small noise is good for quantum computation). Kitaev's surface code.
6. Quantum speed limit/time-energy uncertainty vs symplectic displacement energy.
7. Time-energy uncertainty and quantum computation (Dorit or her student?)
8. Berezin transform, Markov chains, spectral gap, noise.
9. Adiabatic computation, quantum PCP (probabilistically checkable proofs) conjecture
[? under discussion]
10. Noise stability and noise sensitivity of Boolean functions, noisy boson
sampling
11. Connection to quantum field theory (Guy?).
Literature:
Aharonov, D. Quantum computation, In "Annual Reviews of Computational Physics" VI, 1999
(pp. 259-346).
<a href="https://arxiv.org/abs/quant-ph/9812037">https://arxiv.org/abs/quant-ph/9812037</a>
Kalai, G., Three puzzles on mathematics computations, and games, Proc. Int
Congress Math 2018, Rio de Janeiro, Vol. 1 pp. 551–606.
<a href="https://arxiv.org/abs/1801.02602">https://arxiv.org/abs/1801.02602</a>
Nielsen, M.A., and Chuang, I.L., Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000.
Polterovich, L., Symplectic rigidity and quantum mechanics, European Congress of Mathematics, 155–179, Eur. Math. Soc., Zürich, 2018.
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rigidity-and-quantum-mechanics">https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rig...</a>
Polterovich L., and Rosen D., Function theory on symplectic manifolds. American Mathematical Society; 2014. [Chapters 1,9]
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/function-theory-on-symplectic-manifolds">https://sites.google.com/site/polterov/miscellaneoustexts/function-theor...</a>
Wigderson, A., Mathematics and computation, Princeton Univ. Press, 2019.
<a href="https://www.math.ias.edu/files/mathandcomp.pdf">https://www.math.ias.edu/files/mathandcomp.pdf</a>Sun, 27 Oct 2019 12:00:00 +0000Anonymous92999 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze?delta=6" >Kazhdan Sunday seminar: Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze) </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze
Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze)
Abstract: We shall discuss (Weil) cohomology theories for algebraic varieties.
When working with schemes over p-complete rings and taking cohomologies with p-complete coefficients one gets a plurality of such cohomology theories (e'tale, De-Rahm, Crystalline, etc.. ). The comparison between these different cohomology theories is a subtle subject known as "p-adic hodge theory" .
Recently Bhatt and Scholze defined a new such cohomology theory called prismatic cohomology. Remarkably, prismatic cohomology is easier to define than most p-adic cohomology theories and in the same specialized to each of them.The main new tool is the notions of delta-rings and prisms.
We shall start discussing general Weil) cohomology theories for algebraic varieties and give basic examples, we then move to develop the algebra of delta-rings and prisms, we then define the prisamtic site and prismatic cohomology. We shall then continue with comparison theorems and finally some applications Sun, 27 Oct 2019 14:00:00 +0000Anonymous92998 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/analysis-seminar-matania-ben-artzi-huji-tba?delta=0" >Analysis Seminar: Matania Ben-Artzi (HUJI) "TBA"</a>
https://mathematics.huji.ac.il/event/analysis-seminar-matania-ben-artzi-huji-tba
Wed, 11 Dec 2019 10:00:00 +0000Anonymous92348 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows?delta=7" >Kazhdan Sunday seminar: Elon Lindenstrauss "Arithmetic applications of diagonal flows" </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows
Elon Lindenstrauss "Arithmetic applications of diagonal flows"
I will give an introduction to the dynamics of higher rank diagonal flows on homogeneous spaces,
including both the rigidity theorems of such flows and their applications to orbits of arithmetic interest,
in particular CM points and integer points on spheres.
I hope to cover parts of the following papers:
Einsiedler, Manfred ; Lindenstrauss, Elon ; Michel, Philippe ; Venkatesh, Akshay . The distribution of closed geodesics
on the modular surface, and Duke's theorem. Enseign. Math. (2) 58 (2012), no. 3-4, 249--313.
Einsiedler, M., Lindenstrauss, E., Symmetry of entropy in higher rank diagonalizable actions and measure classification.
arXiv e-prints arXiv:1803.07762.
Einsiedler, M. & Lindenstrauss, E. .Joinings of higher rank torus actions on homogeneous spaces. Publ.math.IHES (2019).
<a href="https://doi.org/10.1007/s10240-019-00103-y">https://doi.org/10.1007/s10240-019-00103-y</a>
Khayutin, Ilya . Joint equidistribution of CM points. Ann. of Math. (2) 189 (2019), no. 1, 145--276.
Aka, Menny ; Einsiedler, Manfred ; Shapira, Uri . Integer points on spheres and their orthogonal lattices.
Invent. Math. 206 (2016), no. 2, 379--396.Sun, 27 Oct 2019 09:00:00 +0000Anonymous92997 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil?delta=7" >Kazhdan Sunday seminar: "Computation, quantumness, symplectic geometry, and information" (Gil Kalai, Leonid Polterovich, with participation of Dorit Aharonov and Guy Kindler)</a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil
Tentative syllabus
1. Mathematical models of classical and quantum mechanics.
2. Correspondence principle and quantization.
3. Classical and quantum computation: gates, circuits, algorithms
(Shor, Grover). Solovay-Kitaev. Some ideas of cryptography
4. Quantum noise and measurement, and rigidity of the Poisson bracket.
5. Noisy classical and quantum computing and error correction, threshold theorem- quantum fault tolerance (small noise is good for quantum computation). Kitaev's surface code.
6. Quantum speed limit/time-energy uncertainty vs symplectic displacement energy.
7. Time-energy uncertainty and quantum computation (Dorit or her student?)
8. Berezin transform, Markov chains, spectral gap, noise.
9. Adiabatic computation, quantum PCP (probabilistically checkable proofs) conjecture
[? under discussion]
10. Noise stability and noise sensitivity of Boolean functions, noisy boson
sampling
11. Connection to quantum field theory (Guy?).
Literature:
Aharonov, D. Quantum computation, In "Annual Reviews of Computational Physics" VI, 1999
(pp. 259-346).
<a href="https://arxiv.org/abs/quant-ph/9812037">https://arxiv.org/abs/quant-ph/9812037</a>
Kalai, G., Three puzzles on mathematics computations, and games, Proc. Int
Congress Math 2018, Rio de Janeiro, Vol. 1 pp. 551–606.
<a href="https://arxiv.org/abs/1801.02602">https://arxiv.org/abs/1801.02602</a>
Nielsen, M.A., and Chuang, I.L., Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000.
Polterovich, L., Symplectic rigidity and quantum mechanics, European Congress of Mathematics, 155–179, Eur. Math. Soc., Zürich, 2018.
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rigidity-and-quantum-mechanics">https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rig...</a>
Polterovich L., and Rosen D., Function theory on symplectic manifolds. American Mathematical Society; 2014. [Chapters 1,9]
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/function-theory-on-symplectic-manifolds">https://sites.google.com/site/polterov/miscellaneoustexts/function-theor...</a>
Wigderson, A., Mathematics and computation, Princeton Univ. Press, 2019.
<a href="https://www.math.ias.edu/files/mathandcomp.pdf">https://www.math.ias.edu/files/mathandcomp.pdf</a>Sun, 27 Oct 2019 12:00:00 +0000Anonymous92999 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze?delta=7" >Kazhdan Sunday seminar: Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze) </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze
Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze)
Abstract: We shall discuss (Weil) cohomology theories for algebraic varieties.
When working with schemes over p-complete rings and taking cohomologies with p-complete coefficients one gets a plurality of such cohomology theories (e'tale, De-Rahm, Crystalline, etc.. ). The comparison between these different cohomology theories is a subtle subject known as "p-adic hodge theory" .
Recently Bhatt and Scholze defined a new such cohomology theory called prismatic cohomology. Remarkably, prismatic cohomology is easier to define than most p-adic cohomology theories and in the same specialized to each of them.The main new tool is the notions of delta-rings and prisms.
We shall start discussing general Weil) cohomology theories for algebraic varieties and give basic examples, we then move to develop the algebra of delta-rings and prisms, we then define the prisamtic site and prismatic cohomology. We shall then continue with comparison theorems and finally some applications Sun, 27 Oct 2019 14:00:00 +0000Anonymous92998 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/analysis-seminar-moshe-goldberg-technion-tba?delta=0" >Analysis Seminar: Moshe Goldberg (Technion) "Extending the Spectral Radius to Finite-Dimensional Power-Associative Algebras"</a>
https://mathematics.huji.ac.il/event/analysis-seminar-moshe-goldberg-technion-tba
Title: Extending the Spectral Radius to Finite-Dimensional Power-Associative Algebras
Abstract: The purpose of this talk is to introduce a new concept, the \textit{radius} of elements in arbitrary finite-dimensional power-associative algebras over the field of real or complex numbers. It is an extension of the well known notion of the spectral radius.
As examples, we shall discuss this new radius in the setting of matrix algebras, where it indeed reduces to the spectral radius, and then in the Cayley-Dickson algebras, where it is something quite different.
We shall also describe two applications of this new concept, which are related, respectively, to the Gelfand formula, and to the stability of norms and subnorms.Wed, 18 Dec 2019 10:00:00 +0000Anonymous92923 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/zabrodsky-lecture-1-symplectic-topologist-dynamicist?delta=0" >Zabrodsky Lecture 1: The symplectic topologist as a dynamicist</a>
https://mathematics.huji.ac.il/event/zabrodsky-lecture-1-symplectic-topologist-dynamicist
<p>
The deveolpment of symplectic topology was motivated by Hamiltonian mechanics. It has been particularly successful in addressing one specific aspect, namely fixed points and periodic points of discrete-time Hamiltonian systems. I will explain how such applications work, both in older and more recent examples.
</p>
Thu, 19 Dec 2019 12:30:00 +0000seminarEditor92464 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows?delta=8" >Kazhdan Sunday seminar: Elon Lindenstrauss "Arithmetic applications of diagonal flows" </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-elon-lindenstrauss-arithmetic-applications-diagonal-flows
Elon Lindenstrauss "Arithmetic applications of diagonal flows"
I will give an introduction to the dynamics of higher rank diagonal flows on homogeneous spaces,
including both the rigidity theorems of such flows and their applications to orbits of arithmetic interest,
in particular CM points and integer points on spheres.
I hope to cover parts of the following papers:
Einsiedler, Manfred ; Lindenstrauss, Elon ; Michel, Philippe ; Venkatesh, Akshay . The distribution of closed geodesics
on the modular surface, and Duke's theorem. Enseign. Math. (2) 58 (2012), no. 3-4, 249--313.
Einsiedler, M., Lindenstrauss, E., Symmetry of entropy in higher rank diagonalizable actions and measure classification.
arXiv e-prints arXiv:1803.07762.
Einsiedler, M. & Lindenstrauss, E. .Joinings of higher rank torus actions on homogeneous spaces. Publ.math.IHES (2019).
<a href="https://doi.org/10.1007/s10240-019-00103-y">https://doi.org/10.1007/s10240-019-00103-y</a>
Khayutin, Ilya . Joint equidistribution of CM points. Ann. of Math. (2) 189 (2019), no. 1, 145--276.
Aka, Menny ; Einsiedler, Manfred ; Shapira, Uri . Integer points on spheres and their orthogonal lattices.
Invent. Math. 206 (2016), no. 2, 379--396.Sun, 27 Oct 2019 09:00:00 +0000Anonymous92997 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil?delta=8" >Kazhdan Sunday seminar: "Computation, quantumness, symplectic geometry, and information" (Gil Kalai, Leonid Polterovich, with participation of Dorit Aharonov and Guy Kindler)</a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-computation-quantumness-symplectic-geometry-and-information-gil
Tentative syllabus
1. Mathematical models of classical and quantum mechanics.
2. Correspondence principle and quantization.
3. Classical and quantum computation: gates, circuits, algorithms
(Shor, Grover). Solovay-Kitaev. Some ideas of cryptography
4. Quantum noise and measurement, and rigidity of the Poisson bracket.
5. Noisy classical and quantum computing and error correction, threshold theorem- quantum fault tolerance (small noise is good for quantum computation). Kitaev's surface code.
6. Quantum speed limit/time-energy uncertainty vs symplectic displacement energy.
7. Time-energy uncertainty and quantum computation (Dorit or her student?)
8. Berezin transform, Markov chains, spectral gap, noise.
9. Adiabatic computation, quantum PCP (probabilistically checkable proofs) conjecture
[? under discussion]
10. Noise stability and noise sensitivity of Boolean functions, noisy boson
sampling
11. Connection to quantum field theory (Guy?).
Literature:
Aharonov, D. Quantum computation, In "Annual Reviews of Computational Physics" VI, 1999
(pp. 259-346).
<a href="https://arxiv.org/abs/quant-ph/9812037">https://arxiv.org/abs/quant-ph/9812037</a>
Kalai, G., Three puzzles on mathematics computations, and games, Proc. Int
Congress Math 2018, Rio de Janeiro, Vol. 1 pp. 551–606.
<a href="https://arxiv.org/abs/1801.02602">https://arxiv.org/abs/1801.02602</a>
Nielsen, M.A., and Chuang, I.L., Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000.
Polterovich, L., Symplectic rigidity and quantum mechanics, European Congress of Mathematics, 155–179, Eur. Math. Soc., Zürich, 2018.
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rigidity-and-quantum-mechanics">https://sites.google.com/site/polterov/miscellaneoustexts/symplectic-rig...</a>
Polterovich L., and Rosen D., Function theory on symplectic manifolds. American Mathematical Society; 2014. [Chapters 1,9]
<a href="https://sites.google.com/site/polterov/miscellaneoustexts/function-theory-on-symplectic-manifolds">https://sites.google.com/site/polterov/miscellaneoustexts/function-theor...</a>
Wigderson, A., Mathematics and computation, Princeton Univ. Press, 2019.
<a href="https://www.math.ias.edu/files/mathandcomp.pdf">https://www.math.ias.edu/files/mathandcomp.pdf</a>Sun, 27 Oct 2019 12:00:00 +0000Anonymous92999 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze?delta=8" >Kazhdan Sunday seminar: Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze) </a>
https://mathematics.huji.ac.il/event/kazhdan-sunday-seminar-tomer-schlank-prismatic-cohomology-after-bhatt-and-scholze
Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze)
Abstract: We shall discuss (Weil) cohomology theories for algebraic varieties.
When working with schemes over p-complete rings and taking cohomologies with p-complete coefficients one gets a plurality of such cohomology theories (e'tale, De-Rahm, Crystalline, etc.. ). The comparison between these different cohomology theories is a subtle subject known as "p-adic hodge theory" .
Recently Bhatt and Scholze defined a new such cohomology theory called prismatic cohomology. Remarkably, prismatic cohomology is easier to define than most p-adic cohomology theories and in the same specialized to each of them.The main new tool is the notions of delta-rings and prisms.
We shall start discussing general Weil) cohomology theories for algebraic varieties and give basic examples, we then move to develop the algebra of delta-rings and prisms, we then define the prisamtic site and prismatic cohomology. We shall then continue with comparison theorems and finally some applications Sun, 27 Oct 2019 14:00:00 +0000Anonymous92998 at https://mathematics.huji.ac.il<a href="https://mathematics.huji.ac.il/event/zabrodsky-lecture-2-symplectic-topologist-number-theorist?delta=0" >Zabrodsky Lecture 2: The symplectic topologist as a number theorist</a>
https://mathematics.huji.ac.il/event/zabrodsky-lecture-2-symplectic-topologist-number-theorist
<p>
Most of the complications of classical topology have to do with torsion phenomena, say by looking at homology with modulo p coefficients. In principle, the same is true for symplectic topology, but the implications are only beginning to be explored. A particular impetus is provided by mirror symmetry, which links symplectic topology with arithmetic geometry.
</p>
Mon, 23 Dec 2019 11:00:00 +0000seminarEditor92465 at https://mathematics.huji.ac.il