2018
Jan
25

# Colloquium

- 2018 Jan 18
- 2018 Jan 11
# Colloquium: Andrei Okounkov (Columbia) - "Catching monodromy"

2:30pm to 3:30pm## Location:

Manchester Building (Hall 2), Hebrew University JerusalemMonodromy 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. - 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 JerusalemThe 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 28
# Colloquium: Or Hershkovits (Stanford) - "The Mean Curvature flow and its applications"

2:30pm to 3:30pm## Location:

Manchester Building (Hall 2), Hebrew University JerusalemBeing 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 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 JerusalemSeveral 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 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 JerusalemMirror 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. - 2017 Dec 07
# Colloquium: Nikita Rozenblyum (Chicago) - "String topology and noncommutative geometry"

2:30pm to 3:30pm## Location:

Manchester Building (Hall 2), Hebrew University JerusalemA 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 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 JerusalemSince 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 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 JerusalemI 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.