Events & Seminars

2017 Nov 14

T&G: Shmuel Weinberger (University of Chicago), Periodic transformations on aspherical manifolds

12:00pm to 1:30pm

Location: 

Room 70A, Ross Building, Jerusalem, Israel
Suppose Z/n acts on a manifold, then if it has a fixed point, the natural homomorphism Z/n --> Out(π) (π = the fundamental group) lifts to Aut(π). If π is centreless, and the aspherical manifold is locally symmetric and the action is isometric, the converse holds. We shall discuss the extent to which this observation is geometric and to what extent it's topological. (It will depend on M and it will depend on n). לאירוע הזה יש שיחת וידאו. הצטרף: https://meet.google.com/mcs-bwxr-iza
2018 Jan 02

T&G: Shaofeng Wang (Hebrew University), GIT, symplectic reduction and the Kempf-Ness theorem

1:00pm to 2:30pm

Location: 

Room 63, Ross Building, Jerusalem, Israel
Let G be a group acting on a projective variety. If G is noncompact, the quotient space X/G is in general "bad". In this talk I will discuss two methods to make this quotient "good", i.e. GIT and symplectic reduction. Both methods include the idea of keeping "good orbits" and throwing away "bad orbits". Hilbert-Mumford criterion provides a way to distinguish good orbits (which are called stable orbits) and the Kempf-Ness theorem tells us two methods produce the same quotient space. I will use several examples to show how Hilbert-Mumford criterion and the Kempf-Ness theorem work.
2017 Oct 24

T&G: Asaf Shachar (Hebrew University), Riemannian embeddings of minimal distortion

12:00pm to 1:30pm

Location: 

Room 70A, Ross Building, Jerusalem, Israel
This talk revolves around the question of how close is one Riemannian manifold to being isometrically immersible in another. We associate with every mapping $f:(M,g) \to (N,h)$ a measure of distortion - an average distance of $df$ from being an isometry. Reshetnyak's theorem states that a sequence of mappings between Euclidean domains whose distortion tends to zero has a subsequence converging to an isometry. I will present a generalization of Reshetnyak’s theorem to the general Riemannian setting.
2017 Nov 07

T&G: Ran Tessler (ETH - ITS), Open (CP^1,RP^1) intersection theory: properties, calculations and open Gromov-Witten/Hurwitz corrspondence.

1:00pm to 2:30pm

Location: 

Room 70A, Ross Building, Jerusalem, Israel
We will start be explaining the difficulties in constructing enumerative open Gromov-Witten theories, and mention cases we can overcome these difficulties and obtain a rich enumerative structure. We then restrict to one such case, and define the full genus 0 stationary open Gromov-Witten theory of maps to CP^1 with boundary conditions on RP^1, including descendents, together with its equivariant extension. We fully compute the theory.
2017 Dec 28

Colloquium: Or Hershkovits (Stanford) - "The Mean Curvature flow and its applications"

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
Being the gradient flow of the area functional, the mean curvature flow can be thought of as a greedy algorithm for simplifying embedded shapes. But how successful is this algorithm? In this talk, I will describe three examples for how mean curvature flow, as well as its variants and weak solutions, can be used to achieve this desired simplification. The first is a short time smoothing effect of the flow, allowing to smooth out some rough, potentially fractal initial data.
2017 Nov 09

Colloquium: Nir Lev (Bar Ilan University) - Fourier quasicrystals

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
By a Fourier quasicrystal we mean a pure point measure in R^d, whose Fourier transform is also a pure point measure. This notion was inspired by the experimental discovery of quasicrystalline materials in the middle of 80's. The classical example of such a measure comes from Poisson's summation formula. Which other measures of this type may exist? I will give the relevant background on this problem and present our recent results obtained in joint work with Alexander Olevskii.
2017 Nov 23

Colloquium: Andreas Thom (Dresden) - "Topological methods to solve equations over groups"

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
I will survey various approximation properties of finitely generated groups and explain how they can be used to prove various longstanding conjectures in the theory of groups and group rings. A large class of groups (no group known to be not in the class) is presented that satisfy the Kervaire-Laudenbach Conjecture about solvability of non-singular equations over groups. Our method is inspired by seminal work of Gerstenhaber-Rothaus, which was the key to prove the Kervaire-Laudenbach Conjecture for residually finite groups.
2018 Jan 04

Colloquium: Joachim König (Universität Würzburg) - "Specialization of Galois coverings over number fields"

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
The inverse Galois problem (over number fields k) is one of the central problems in algebraic number theory. A classical approach to it is via specialization of Galois coverings: Hilbert’s irreducibility theorem guarantees the existence of infinitely many specialization values in k such that the Galois group of the specialization equals the Galois group of the covering. I will consider problems related to the inverse Galois problem which can be attacked using the specialization approach.
2017 Dec 07

Colloquium: Nikita Rozenblyum (Chicago) - "String topology and noncommutative geometry"

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
A classical result of Goldman states that character variety of an oriented surface is a symplectic algebraic variety, and that the Goldman Lie algebra of free loops on the surface acts by Hamiltonian vector fields on the character variety. I will describe a vast generalization of these results, including to higher dimensional manifolds where the role of the Goldman Lie algebra is played by the Chas-Sullivan string bracket in the string topology of the manifold. These results follow from a general statement in noncommutative geometry.
2017 Dec 21

Colloquium: Alex Lubotzky (HUJI) - "Groups approximation, stability and high dimensional expanders"

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
Several well-known open questions (such as: are all groups sofic or hyperlinear?) have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)? In the case of U(n), the question can be asked with respect to different metrics andnorms. We answer, for the first time, one of these versions, showing that there exist fintely presented groups which arenot approximated by U(n) with respect to the Frobenius (=L_2) norm.
2017 Nov 16

Colloquium: John R. Klein (Wayne State U.) - "Algebraic Topology and Fluctuations"

2:40pm to 3:40pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
This talk will investigate a certain class of continuous time Markov processes using machinery from algebraic topology. To each such process, we will associate a homological observable, the average current, which is a measurement of the net flow of probability of the system. We show that the average current quantizes in the low temperature limit. We also explain how the quantized version admits a topological description.
2018 Jan 11

Colloquium: Andrei Okounkov (Columbia) - "Catching monodromy"

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
Monodromy of linear differential and difference equations is a very old and classical object, which may be seen as a far-reaching generalization of the exponential map of a Lie group. While general properties of this map may studied abstractly, for certain very special equations of interest in enumerative geometry, representation theory, and also mathematical physics, it is possible to describe the monodromy "explicitly", in certain geometric and algebraic terms. I will explain one such recent set of ideas, following joint work with M. Aganagic and R. Bezrukavnikov.

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