Kazhdan Sunday Seminars

The Kazhdan Sunday seminar meets on Sundays at 11:00-13:00 and 15:00-17:00 in room 70 of the Ross Building.

2020 Jan 26

Kazhdan Sunday seminar: Tomer Schlank "Prismatic cohomology" (after Bhatt and Scholze)

Repeats every week every Sunday until Sat Feb 01 2020 except Sun Oct 27 2019.

4:00pm to 6:00pm

Location:

Ross 70

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" .

2019 Oct 27

Kazhdan Sunday seminar: Elon Lindenstrauss "Arithmetic applications of diagonal flows"

Repeats every week every Sunday until Sat Feb 01 2020 except Sun Oct 27 2019.

11:00am to 1:00pm

Location:

Ross 70

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

2019 Oct 27

Kazhdan Sunday seminar: "Computation, quantumness, symplectic geometry, and information" (Gil Kalai, Leonid Polterovich, with participation of Dorit Aharonov and Guy Kindler)

Repeats every week every Sunday until Sat Feb 01 2020 except Sun Dec 29 2019.

2:00pm to 4:00pm

Location:

Ross 70

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.

2019 Mar 18

Special course: A. Goncharov (Yale, visiting Einstein Institute of Mathematics) "Quantum geometry of moduli spaces of local systems on surfaces and representation theory"

Repeats every week every Monday until Mon Apr 29 2019 except Mon Apr 22 2019.

4:00pm to 6:00pm

Location:

Ross 70

Abstract. This is a joint work with Linhui Shen.
A decorated surface is an oriented surface with punctures and a finite collection of special points on the boundary, considered modulo isotopy.
Let G be a split adjoint group. We introduce a moduli space Loc(G,S) of G-local systems on a decorated surface S, which reduces to the character variety when S has no boundary, and quantize it.

2019 Mar 10

Zlil Sela and Alex Lubotzky "Model theory of groups"

Repeats every week every Sunday until Sat Jun 29 2019 except Sun Apr 21 2019.

11:00am to 1:00pm

Zlil Sela and Alex Lubotzky "Model theory of groups"
In the first part of the course we will present some of the main results in the theory of free,
hyperbolic and related groups, many of which appear as lattices in rank one simple Lie groups
We will present some of the main objects that are used in studying the theory of these groups,
and at least sketch the proofs of some of the main theorems.
In the second part of the course, we will talk about the model theory of lattices in high rank simple Lie groups.

2019 Mar 10

Ari Shnidman "Geometric expressions for derivatives of L-functions of automorphic forms" (after Yun and Zhang)

Repeats every week every Sunday until Sun Jun 23 2019 except Sun Apr 21 2019.

2:00pm to 4:00pm

Yun and Zhang compute the Taylor series expansion of an automorphic L-function over a function field, in terms of intersection pairings of certain algebraic cycles on the so-called moduli stack of shtukas. This generalizes the Waldspurger and Gross-Zagier formulas, which concern the first two coefficients.

2018 Nov 11

Kazhdan seminar: Tomer Schlank "The Nonabelian Chabauty Method"

12:00pm to 2:00pm

Location:

Ross 70A

Abstract:
The Chabauty method is a remarkable tool which employs p-adic analitic methods (in particular Colman integration.) To study rational points on curves. However the method can be applied only when the genus of the curve in question is larger than its Mordell-Weil rank. Kim developed a sophisticated "nonableian" generalisation.
We shall present the classical methid, and give an approachable introduction to Kim's method.
I'm basically going to follow http://math.mit.edu/nt/old/stage_s18.html

2018 Nov 25

Kazhdan seminar: Karim Adiprasito "Positivity in combinatorics and beyond"

3:00pm to 5:00pm

Location:

Ross 70A

Abstract: I will discuss applications of algebraic results to combinatorics, focusing in particular on Lefschetz theorem, Decomposition theorem and Hodge Riemann relations. Secondly, I will discuss proving these results combinatorially, using a technique by McMullen and extended by de Cataldo and Migliorini. Finally, I will discuss Lefschetz type theorems beyond positivity.
Recommended prerequisites: basic commutative algebra

2019 Jan 13