Eventss

2017 Dec 26

T&G: Or Hershkovits (Stanford), Uniqueness of mean curvature flow through (some) singularities

1:00pm to 2:30pm

Location: 

Room 63, Ross Building, Jerusalem, Israel
Abstract: Given a smooth compact hypersurface in Euclidean space, one can show that there exists a unique smooth evolution starting from it, existing for some maximal time. But what happens after the flow becomes singular? There are several notions through which one can describe weak evolutions past singularities, with various relationship between them. One such notion is that of the level set flow.
2017 Oct 31

T&G: Pavel Giterman (Hebrew University), Descendant Invariants in Open Gromov Witten Theory

12:00pm to 1:30pm

Location: 

Room 70A, Ross Building, Jerusalem, Israel
In this talk we will consider the question of defining descendant invariants in open Gromov-Witten theory. In the closed Gromov-Witten theory, descendant invariants are constructed from Chern classes of certain tautological lines bundles which live on the moduli space of stable curves. The intersection numbers obtained from those classes (and other classes) can be incorporated in a generating function that satisfies various partial differential equations reflecting recurrence relations and which can sometimes be used to calculate the numbers explicitly.
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.
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.
2018 Jan 25

Ostrowski Prize Lecture - Akshay Venkatesh (Stanford) - Period maps and Diophantine problems

2:15pm to 3:45pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
Given a family of complex algebraic varieties parameterized by a base variety B there is an associated period mapping, which (at least locally) goes from B to a certain flag variety. However, although both the source and target are algebraic varieties,
this period map is of a transcendental nature.
I will explain joint work with Brian Lawrence which shows how the transcendence of the period mapping
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.
2017 Nov 30

Colloquium: Doron Puder (Tel Aviv) - "Matrix Integrals, Graphs on Surfaces and Mapping Class Group"

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
Since the 1970's, Physicists and Mathematicians who study random matrices in the standard models of GUE or GOE, are aware of intriguing connections between integrals of such random matrices and enumeration of graphs on surfaces. We establish a new aspect of this theory: for random matrices sampled from the group U(n) of Unitary matrices. The group structure of these matrices allows us to go further and find surprising algebraic quantities hidden in the values of these integrals. The talk will be aimed at graduate students, and all notions will be explained.
2017 Dec 14

Colloquium: Yoel Groman (Columbia) - "Mirror symmetry for toric Calabi Yau 3-folds"

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
Mirror symmetry is a far reaching duality relating symplectic geometry on a given manifold to complex geometry on a completely different manifold - its mirror. Toric Calabi Yau manifolds are a large family of examples which which have served as a testing ground for numerous ideas in the study of mirror symmetry. I will prove homological mirror symmetry when the symplectic side is a toric Calabi-Yau 3-fold. I will aim to explain geometrically why the mirror of a toric Calabi Yau takes the particular form it does.

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