Everytopic Seminar - Fall 2014
Room 226, Goldsmith building
Organizer: Olivier Bernardi
The Everytopic Seminar is a seminar aimed at a broad audience of mathematicians.
The talks are 80 minutes long. The first 40 minutes of the talk should be given in a
colloquium style, and should be accessible to faculty and graduate students
from any field of mathematics. It should allow everyone to grasp the content and
significance of the results being discussed. The last 40 minutes should be in
the style of a research seminar, providing the audience with a deeper understanding
of the results as well as some details of the proofs.
Friday September 19
Speaker: Ilya Vinogradov (University of Bristol)
Title: Effective Ratner Theorem for ASL(2, R) and the gaps of the sequence
\sqrt n modulo 1
Abstract: Let G=SL(2,\R)\ltimes R^2 and Gamma=SL(2,Z)\ltimes Z^2. Building on
recent work of Strombergsson we prove a rate of equidistribution for the
orbits of a certain 1-dimensional unipotent flow of Gamma\G, which projects to
a closed horocycle in the unit tangent bundle to the modular surface. We use
this to answer a question of Elkies and McMullen by making effective the
convergence of the gap distribution of sqrt n mod 1.
Friday October 3
Speaker: Andreas Arvanitoyeorgos (University of Patras and Tufts University)
Title: Aspects of homogeneous geometry with application to invariant Einstein metrics
Abstract: According to F. Klein's Erlanger program geometry is the study of those properties of a space M, which are invariant under the action of a group G. When M is a smooth manifold and G is a Lie group which acts transitively on M, then M can be identified with the quotient space G/H, where H is the isotropy subgroup of a fixed point p of M. In this case, and under some assumptions, the geometry of the space M (e.g. curvature or geodesics) reduces to the study of the pair (g, h), where g, h are the Lie algebras of G and H respectively.
In the first part of the talk I will give some details on the theory of homogeneous spaces and Lie groups and then I will discuss some recent results on homogeneous Einstein metrics on two important class of homogeneous spaces, namely flag manifolds and Stiefel manifolds.
Friday October 10
Speaker: Stephen Hermes (Wellesley College)
Title: Maximal Green Sequences and Semi-Invariant Pictures
Abstract: Quiver mutation is a combinatorial process with several striking connections to diverse areas of mathematics including (among others) representation theory, mathematical physics, and geometry. Maximal green sequences are particular sequences of quiver mutations originally introduced by Keller in order to give a combinatorial description of the (refined) DT-invariants of 3-Calabi-Yau categories. Little is known about the enumeration of maximal green sequences in general. In particular, it is unknown if any quiver admits only finitely many maximal green sequences.
This talk is a report on work in progress with Brüstle, Igusa, and Todorov to interpret maximal green sequences in terms of the invariant theory of quiver varieties using ``semi-invariant pictures.'' Using the geometry of these pictures we give an alternative proof of a theorem of Brüstle-Dupont-Pérotin stating that so-called ``tame'' quivers admit only finitely many maximal green sequences.
Friday October 24
Speaker: Evgeniy Zorin (University of York)
Title: Mahler numbers and Diophantine approximation
Abstract: Mahler numbers originate in works of Kurt Mahler on transcendence. Their Diophantine properties have a surprising link with theoretical computer science. We will discuss the state of the art as well as the recent advancements in this area.
Friday October 31
Speaker: Jason Miller (MIT)
Friday November 7
Speaker: Aaron Pixton (Harvard)
Friday November 14
Speaker: Jonathan Novak (MIT)
Friday November 21
Speaker: Vidya Venkateswaran (MIT)
Map of Brandeis University - the Department of Mathematics (Goldsmith building) is U24 on this map.
For further information please contact:
Olivier Bernardi (bernardi at brandeis dot edu).