Seminars and Colloquia by Series

Stochastic models for the transmission and establishment of HIV infection

Series
Mathematical Biology Seminar
Time
Wednesday, March 27, 2019 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dan Coombs – UBC (visiting Emory) –
The likelihood of HIV infection following risky contact is believed to be low. This suggests that the infection process is stochastic and governed by rare events. I will present mathematical branching process models of early infection and show how we have used them to gain insights into the duration of the undetectable phase of HIV infection, the likelihood of success of pre- and post-exposure prophylaxis, and the effects of prior infection with HSV-2. Although I will describe quite a bit of theory, I will try to keep giant and incomprehensible formulae to a minimum.

Joint GT-UGA Seminar at UGA - A spectral sequence from Khovanov homology to knot Floer homology

Series
Geometry Topology Seminar
Time
Monday, March 25, 2019 - 14:30 for 1 hour (actually 50 minutes)
Location
Boyd
Speaker
Nathan Dowlin – Dartmouth
Khovanov homology and knot Floer homology are two knot invariants which are defined using very different techniques, with Khovanov homology having its roots in representation theory and knot Floer homology in symplectic geometry. However, they seem to contain a lot of the same topological data about knots. Rasmussen conjectured that this similarity stems from a spectral sequence from Khovanov homology to knot Floer homology. In this talk I will give a construction of this spectral sequence. The construction utilizes a recently defined knot homology theory HFK_2 which provides a framework in which the two theories can be related.

Cohen-Macaulayness of invariant rings is determined by inertia groups

Series
Algebra Seminar
Time
Monday, March 25, 2019 - 12:50 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ben Blum-Smith – NYU

If a finite group $G$ acts on a Cohen-Macaulay ring $A$, and the order of $G$ is a unit in $A$, then the invariant ring $A^G$ is Cohen-Macaulay as well, by the Hochster-Eagon theorem. On the other hand, if the order of $G$ is not a unit in $A$ then the Cohen-Macaulayness of $A^G$ is a delicate question that has attracted research attention over the last several decades, with answers in several special cases but little general theory. In this talk we show that the statement that $A^G$ is Cohen-Macaulay is equivalent to a statement quantified over the inertia groups for the action of G$ on $A$ acting on strict henselizations of appropriate localizations of $A$. In a case of long-standing interest—a permutation group acting on a polynomial ring—we show how this can be applied to find an obstruction to Cohen-Macaulayness that allows us to completely characterize the permutation groups whose invariant ring is Cohen-Macaulay regardless of the ground field. This is joint work with Sophie Marques.

Mixing and the local limit theorem for hyperbolic dynamical systems

Series
Math Physics Seminar
Time
Friday, March 15, 2019 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Peter Nandori – University of Maryland –
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.

The interaction of gaps with the boundary in dimer systems --- a heat flow conjecture

Series
Math Physics Seminar
Time
Friday, March 15, 2019 - 14:45 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Mihai Ciucu – Mathematics Department, Indiana University –
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).

Schubert Galois Groups

Series
Algebra Seminar
Time
Friday, March 15, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Frank Sottile – Texas A&M
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.

Divisors on metric graphs and constructing tropicalizations of Mumford curves

Series
Student Algebraic Geometry Seminar
Time
Friday, March 15, 2019 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Trevor Gunn – Georgia Tech
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.

Clustered coloring for old coloring conjectures

Series
ACO Alumni Lecture
Time
Thursday, March 14, 2019 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Chun-Hung Liu – Texas A&M

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.

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