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Series: Graph Theory Seminar

Let G be a graph containing 5 different vertices a0, a1, a2, b1 and
b2. We say that (G, a0, a1, a2, b1, b2) is feasible if G contains
disjoint connected subgraphs G1, G2, such that {a0, a1, a2}⊆V(G1) and
{b1, b2}⊆V(G2). In this talk, we will introduce
ideal frames, slim connectors and fat connectors. We will first deal
with the ideal frames without fat connectors, by studying 3-edge and
5-edge configurations. Joint work with Changong Li, Robin Thomas, and
Xingxing Yu.

Thursday, November 2, 2017 - 11:05 ,
Location: Skiles 006 ,
Joel Spencer ,
Courant Institute, New York University ,
Organizer: Lutz Warnke

Traditional Erdos Magic (a.k.a. The Probabilistic Method) proves the existence of an object with certain properties by showing that a random (appropriately defined) object will have those properties with positive probability. Modern Erdos Magic analyzes a random process, a random (CS take note!) algorithm. These, when successful, can find a "needle in an exponential haystack" in polynomial time. We'll look at two particular examples, both involving a family of n-element sets under suitable side conditions. The Lovasz Local Lemma finds a coloring with no set monochromatic. A result of this speaker finds a coloring with low discrepency. In both cases the original proofs were not implementable but Modern Erdos Magic finds the colorings in polynomial times. The methods are varied. Basic probability and combinatorics. Brownian Motion. Semigroups. Martingales. Recursions ... and Tetris!

Series: School of Mathematics Colloquium

Series: Research Horizons Seminar

The talk will include a crash course on infinite dimensional
topology, with applications to various topological properties of the
space of congruence classes of convex bodies in the Euclidean space.

Series: Analysis Seminar

The bispectral problem concerns the construction and the classification
of operators possessing a symmetry between the space and spectral
variables. Different versions of this problem can be solved using
techniques from integrable systems, algebraic geometry, representation
theory, classical orthogonal polynomials, etc. I will review the problem
and some of these connections and then discuss new results related to
the generic quantum superintegrable system on the sphere.

Monday, October 30, 2017 - 17:15 ,
Location: Skiles 005 ,
Spencer Bloch ,
University of Chicago ,
Organizer: Joseph Rabinoff

Golyshev and Zagier found an interesting new source of periods associated to (eventually inhomogeneous) solutions generated by the Frobenius method for Picard Fuchs equations in the neighborhood of singular points with maximum unipotent monodromy. I will explain how this works, and how one can associate "motivic Gamma functions" and generalized Beilinson style variations of mixed Hodge structure to these solutions. This is joint work with M. Vlasenko.

Monday, October 30, 2017 - 16:05 ,
Location: Skiles 005 ,
Bjorn Poonen ,
Massachusetts Institute of Technology ,
Organizer: Joseph Rabinoff

The function field case of the strong uniform boundedness conjecturefor torsion points on elliptic curves reduces to showing thatclassical modular curves have gonality tending to infinity.We prove an analogue for periodic points of polynomials under iterationby studying the geometry of analogous curves called dynatomic curves.This is joint work with John R. Doyle.

Series: Geometry Topology Seminar

Heegaard Floer theory provides a powerful suite of tools for studying 3-manifolds and their subspaces. In 2006, Ozsvath, Szabo and Thurston defined an invariant of transverse knots which takes values in a combinatorial version of this theory for knots in the 3—sphere. In this talk, we discuss a refinement of their combinatorial invariant via branched covers and discuss some of its properties. This is joint work with Mike Wong.

Series: Math Physics Seminar

During the last few years there has been a systematic pursuit for sharp estimates of the energy components of atomic systems in terms of their single particle density. The common feature of these estimates is that they include corrections that depend on the gradient of the density. In this talk I will review these results. The most recent result is the sharp estimate of P.T. Nam on the kinetic energy. Towards the end of my talk I will present some recent results concerning geometric estimates for generalized Poincaré inequalities obtained in collaboration with C. Vallejos and H. Van Den Bosch. These geometric estimates are a useful tool to estimate the numerical value of the constant of Nam's gradient correction term.

Friday, October 27, 2017 - 15:00 ,
Location: Skiles 154 ,
Hassan Attarchi ,
Georgia Tech ,
Organizer:

This presentation is about the results of a paper by Y. Sinai in
1970. Here, I will talk about dynamical systems which resulting from the
motion of a material point in domains with strictly convex boundary,
that is, such that the operator of the second quadratic form is
negative-definite at each point of the boundary, where the boundary is
taken to be equipped with the field of inward normals. It was proved
that such systems are ergodic and are K-systems. The basic method of
investigation is the construction of transversal foliations for such
systems and the study of their properties.