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Series: Geometry Topology Seminar

Series: Math Physics Seminar

We present a convenient joint generalization of mixing and the local

central limit theorem which we call MLLT. We review results on the MLLT

for hyperbolic maps and present new results for hyperbolic flows. Then

we apply these results to prove global mixing properties of some

mechanical systems. These systems include various versions of the

Lorentz gas (periodic one; locally perturbed; subject to external

fields), the Galton board and pingpong models. Finally, we present

applications to random walks in deterministic scenery. This talk is

based on joint work with D. Dolgopyat and partially with M. Lenci.

Series: Math Physics Seminar

We consider a triangular gap of side two in a 90 degree angle on the triangular lattice with mixed boundary conditions: a constrained, zig-zag boundary along one side, and a free lattice line boundary along the other. We study the interaction of the gap with thecorner as the rest of the angle is completely filled with lozenges. We show that the resulting correlation is governed by the product of the distances between the gap and its three images in the sides of the angle. This, together with a few other results we worked out previously, provides evidence for a unified way of understanding the interaction of gaps with the boundary under mixed boundary conditions, which we present as a conjecture. Our conjecture is phrased in terms of the steady state heat flow problem in a uniform block of material in which there are a finite number of heat sources and sinks. This new physical analogy is equivalent in the bulk to the electrostatic analogy we developed in previous work, but arises as the correct one for the correlation with the boundary.The starting point for our analysis is an exact formula we prove for the number of lozenge tilings of certain trapezoidal regions with mixed boundary conditions, which is equivalent to a new, multi-parameter generalization of a classical plane partition enumeration problem (that of enumerating symmetric, self-complementary plane partitions).

Series: Algebra Seminar

Problems from enumerative geometry have Galois groups. Like those from field extensions, these Galois groups reflect the internal structure of the original problem. The Schubert calculus is a class of problems in enumerative geometry that is very well understood, and may be used as a laboratory to study new phenomena in enumerative geometry.I will discuss this background, and sketch a picture that is emerging from a sustained study of Schubert problems from the perspective of Galois theory. This includes a conjecture concerning the possible Schubert Galois groups, a partial solution of the inverse Galois problem, as well as glimpses of the outline of a possible classification of Schubert problems for their Galois groups.

Friday, March 15, 2019 - 12:00 ,
Location: Skiles 006 ,
Trevor Gunn ,
Georgia Tech ,
Organizer: Trevor Gunn

I will introduce briefly the notion of Berkovich analytic spaces and certain metric graphs associated to them called the skeleton. Then we will describe divisors on metric graphs and a lifting theorem that allows us to find tropicalizations of curves in P^3. This is joint work with Philipp Jell.

Series: ACO Alumni Lecture

Hadwiger (Hajos and Gerards and Seymour, respectively) conjectured that the vertices of every graph with no K_{t+1} minor (topological minor and odd minor, respectively) can be colored with t colors such that any pair of adjacent vertices receive different colors. These conjectures are stronger than the Four Color Theorem and are either wide open or false in general. A weakening of these conjectures is to consider clustered coloring which only requires every monochromatic component to have bounded size instead of size 1. It is known that t colors are still necessary for the clustered coloring version of those three conjectures. Joint with David Wood, we prove a series of tight results about clustered coloring on graphs with no subgraph isomorphic to a fixed complete bipartite graph. These results have a number of applications. In particular, they imply that the clustered coloring version of Hajos' conjecture is true for bounded treewidth graphs in a stronger sense: K_{t+1} topological minor free graphs of bounded treewidth are clustered t-list-colorable. They also lead to the first linear upper bound for the clustered coloring version of Hajos' conjecture and the currently best upper bound for the clustered coloring version of the Gerards-Seymour conjecture.

Series: Other Talks

Chun-Hung will discuss his employment experience as an ACO alummus. The conversations will take place over coffee.

Series: Stochastics Seminar

Series: Graph Theory Working Seminar

Erdős

and Nešetřil conjectured in 1985 that every graph with maximum degree Δ

can be strong edge colored using at most 5/4 Δ^2 colors. The conjecture

is still open for Δ=4. We show the conjecture is true when an edge cut

of size 1 or 2 exists, and in certain cases when an edge cut of size 4

or 3 exists.

Series: High Dimensional Seminar

We will try to address a few universality questions for the behavior of large random matrices over finite fields, and then present a minimal progress on one of these questions.