Events & Seminars

2021 Jan 05

Dynamics seminar: Balasz Barany (BME) On the Ahlfors regularity of planar self-affine sets

2:00pm to 3:00pm


Abstract: In this talk, we study the Ahlfors regularity of planar self-affine sets under natural conditions: strong separation condition, strong irreducibility and proximality. Not surprisingly, if the dimension is strictly larger than 1, the set is never Ahlfors regular. In case if the dimension is less than or equal to 1 under the extra condition of dominated splitting, we show that the Ahfors regularity is equivalent to the positive proper dimensional Hausdorff measure and to positive proper dimensional Hausdorff measure of the projections in every Furstenberg direction.
2020 Dec 03

Cancelled - Basic Notions: Zeev Rudnik "The Robin eigenvalue problem: statistics and arithmetic"

4:00pm to 5:15pm

Location: 

Zoom
Abstract:  

Robin boundary conditions are used in heat conductance theory to interpolate between a perfectly insulating boundary, described by Neumann boundary conditions, and a temperature fixing boundary, described by Dirichlet boundary conditions.  I have recently started to explore the statistics of these Robin eigenvalues for planar domains, and the fluctuations of the gaps between the Robin and Neumann spectrum, in part driven by numerical experimentation.

2020 Nov 19

Basic Notions: Jake Solomon "Geometric stability"

4:00pm to 5:15pm

Abstract: Thestudy of geometric stability begins with Mumford's geometric invariant theory.The Kempf-Ness theorem establishes a connection between geometric invarianttheory and symplectic quotients. An infinite dimensional analog of theKempf-Ness theorem leads to a deep connection between algebraic geometricstability and special metric geometries. Examples of this connection includethe work of Donaldson and Uhlenbeck-Yau on the Kobayashi-Hitchin correspondenceand work of Yau, Tian, Donaldson and many others on extremal Kahler metrics.

2020 Nov 26

Basic Notions: Zeev Rudnik "The Robin eigenvalue problem: statistics and arithmetic"

4:00pm to 5:15pm

Location: 

Zoom
Abstract:  Robin boundary conditions are used in heat conductance theory to interpolate between a perfectly insulating boundary, described by Neumann boundary conditions, and a temperature fixing boundary, described by Dirichlet boundary conditions.  I have recently started to explore the statistics of these Robin eigenvalues for planar domains, and the fluctuations of the gaps between the Robin and Neumann spectrum, in part driven by numerical experimentation.
2020 Nov 18

Analysis Seminar: Hynek Kovarik (Brescia) "Absence of positive eigenvalues of magnetic Schroedinger operators"

12:00pm to 1:00pm


ABSTRACT:
We study sufficient conditions for the absence of positive eigenvalues of magnetic Schroedinger operators in R^n. In our main result we prove the absence of eigenvalues above certain threshold energy which depends explicitly on the magnetic and electric field. A comparison with the examples of Miller-Simon shows that our result is sharp as far as the decay of the magnetic field is concerned.
The talk is based on a joint work with Silvana Avramska-Lukarska and Dirk Hundertmark.
2020 Nov 11

Analysis Seminar: Adam Dor-On (Copenhagen) "Operator algebras for subshifts and random walks"

12:00pm to 1:00pm

Location: 

zoom

Abstract:

There is a rich history of studying dynamical systems through the lens of operator algebras, and particularly through C*-algebras. For instance, in the work of Giordano, Matui, Putnam and Skau, C*-algebras were used as a key tool for classifying Cantor minimal $\mathbb{Z}^d$ systems up to various notions of orbit equivalence. Another successful study was conducted by Cuntz and Krieger, where subshifts of finite type (SFTs) are interpreted through C*-algebras of directed graphs, and invariants studied in symbolic dynamics naturally arise from these C*-algebras.

2020 Nov 12

Basic Notions: Jake Solomon "Geometric stability"

4:00pm to 5:15pm

Abstract: The study of geometric stability begins with Mumford's geometric invariant theory. The Kempf-Ness theorem establishes a connection between geometric invariant theory and symplectic quotients. An infinite-dimensional analog of the Kempf-Ness theorem leads to a deep connection between algebraic-geometric stability and special metric geometries. Examples of this connection include the work of Donaldson and Uhlenbeck-Yau on the Kobayashi-Hitchin correspondence and work of Yau, Tian, Donaldson, and many others on extremal Kahler metrics.

2020 Oct 25

Kazhdan seminar: Yoel Groman and Jake Solomon "Stability conditions"

Repeats every week every Sunday until Sun Jan 17 2021 .
4:00pm to 6:00pm

4:00pm to 6:00pm
4:00pm to 6:00pm
4:00pm to 6:00pm
4:00pm to 6:00pm
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4:00pm to 6:00pm
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4:00pm to 6:00pm

Abstract: We will discuss stability conditions on triangulated categories following the work of Douglas and Bridgeland. Concrete examples of stability conditions will be given from symplectic and algebraic geometry, which will also illustrate mirror symmetry. An effort will be made to give a gentle introduction to the relevant background material from category theory, symplectic geometry and algebraic geometry.
2020 Dec 08

Dynamics seminar: Erez Nesharim (HUJI) Approximation by algebraic numbers and homogeneous dynamics

2:00pm to 3:00pm

Abstract: Diophantine approximation quantifies the density of the rational numbers in the real line. The extension of this theory to algebraic numbers raises many natural questions. I will focus on a dynamical resolution to Davenport's problem and show that there are uncountably many badly approximable pairs on the parabola. The proof uses the Kleinbock--Margulis uniform estimate for nondivergence of nondegenerate curves in the space of lattices and a variant of Schmidt's game.
2020 Nov 24

Dynamics seminar: Zemer Kosloff (HUJI) Sinai factors of nonsingular Bernoulli shifts

2:00pm to 3:00pm

Abstract: We show that some examples of type-III:1 Bernoulli shifts on two symbols have a factor that is equivalent to an independent and identically distributed system and prove that there are type-III:1 Bernoulli shifts of every possible ergodic index. The latter implies that the classification of type III Bernoulli shifts according to metric isomorphism is more subtle than its classical counterpart (Ornstein theory).


This is joint work with Terry Soo. 

2020 Oct 28

Logic Seminar - Binyamin Riahi

11:15am to 1:00pm

Location: 

Zoom: Meeting ID: 853 4322 9339, Passcode: 5m901l

Monadic stability and growth rates of ω-categorical structures



Abstract: We will present the following work by Samuel Braunfeld. 

For M ω-categorical and stable, we investigate the growth
rate of M, i.e. the number of orbits of Aut(M) on n-sets, or equivalently the number of n-substructures of M after performing quantifier
elimination. We show that monadic stability corresponds to a gap in
the spectrum of growth rates, from slower than exponential to faster
2020 Oct 28

Analysis seminar: Hans Knüpfer (Heidelberg) — Γ-limit for zigzag domain walls in thin ferromagnetic films

12:00pm to 1:00pm

Charged domain walls are a type of transition layers in thin ferromagnetic films which appear due to global topological constraints. The underlying micromagnetic energy is determined by a competition between a diffuse interface energy and the long-range magnetostatic interaction. The underlying model is non-convex and vectorial. In the macroscopic limit we show that the energy Γ-converges to a limit model where jump discontinuities of the magnetization are penalized anisotropically. In particular, we identify a supercritical regime which allows for tangential variation of the domain walls.
2020 Oct 18

Kazhdan seminar: Yoel Groman and Jake Solomon "Stability conditions"

Repeats every week every Sunday until Sat Oct 24 2020 .
4:00pm to 6:00pm


Abstract: We will discuss stability conditions on triangulated categories following the work of Douglas and Bridgeland. Concrete examples of stability conditions will be given from symplectic and algebraic geometry, which will also illustrate mirror symmetry. An effort will be made to give a gentle introduction to the relevant background material from category theory, symplectic geometry and algebraic geometry.
2020 Oct 18

Kazhdan seminar : Ari Shnidman "Fundamental lemmas and Fourier transform"

Repeats every week every Sunday until Sun Jan 17 2021 .
11:00am to 1:00pm

11:00am to 1:00pm
11:00am to 1:00pm
11:00am to 1:00pm
11:00am to 1:00pm
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11:00am to 1:00pm
11:00am to 1:00pm
11:00am to 1:00pm

Abstract: A fundamental lemma is an identity relating p-adic integrals on two different groups. These pretty identities fit into a larger story of trace formulas and special values of L-functions.  Our goal is to present recent work of Beuzart-Plessis on the Jacquet-Rallis fundamental lemma, comparing integrals on GL(n) and U(n).
2020 Oct 18

Kazhdan seminar: Tomer Schank "Sheaves with nilpotent support"

Repeats every week every Sunday until Sun Jan 17 2021 .
2:00pm to 4:00pm

2:00pm to 4:00pm
2:00pm to 4:00pm
2:00pm to 4:00pm
2:00pm to 4:00pm
2:00pm to 4:00pm
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2:00pm to 4:00pm
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2:00pm to 4:00pm

Abstract: Given a smooth and proper curve X and a reductive group G one can consider the stack Bun_{G,X} of principal G-bundles on X. This stack has an important role in Algebraic Geometry and Representation Theory especially with regard to the Langlands program. We shall study the geometry of Bun_{G,X} and the category 
D(G,X) of constructible  sheaves on Bun_{G,X}. We shall be especially interested in the subcategory D_{nil}(G,X) of sheaves with nilpotent singular support.

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