Seminars and Colloquia by Series

Joint GT-UGA Seminar at GT - Knot Traces and the Slice Genus

Series
Geometry Topology Seminar
Time
Monday, February 25, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Lisa Piccirillo – UT Austin
Smooth simply connected 4-manifolds can admit second homology classes not representable by smoothly embedded spheres; knot traces are the prototypical example of 4-manifolds with such classes. I will show that there are knot traces where the minimal genus smooth surface generating second homology is not of the canonical type, resolving question 1.41 on the Kirby problem list. I will also use the same tools to show that Conway knot does not bound a smooth disk in the four ball, which completes the classification of slice knots under 13 crossings and gives the first example of a non-slice knot which is both topologically slice and a positive mutant of a slice knot.

Random perturbations of dynamical systems

Series
CDSNS Colloquium
Time
Monday, February 25, 2019 - 11:15 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Yun Yang – City Univ. NY
The real world is inherently noisy, and so it is natural to consider the random perturbations of deterministic dynamical systems and seek to understand the corresponding asymptotic behavior, i.e., the phenomena that can be observed under long-term iteration. In this talk, we will study the random perturbations of a family of circle maps $f_a$. We will obtain, a checkable, finite-time criterion on the parameter a for random perturbation of $f_a$ to exhibit a unique, and thus ergodic, stationary measure.

Field electron emission and the Fowler-Nordheim equation

Series
Math Physics Seminar
Time
Friday, February 22, 2019 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ian Jauslin – Princeton University –
Consider a metallic field emitter shaped like a thin needle, at the tip of which a large electric field is applied. Electrons spring out of the metal under the influence of the field. The celebrated and widely used Fowler-Nordheim equation predicts a value for the current outside the metal. In this talk, I will show that the Fowler-Nordheim equation emerges as the long-time asymptotic solution of a Schrodinger equation with a realistic initial condition, thereby justifying the use of the Fowler Nordheim equation in real setups. I will also discuss the rate of convergence to the Fowler-Nordheim regime.

spectral equivalence classes based on isospectral reductions

Series
Dynamical Systems Working Seminar
Time
Friday, February 22, 2019 - 03:05 for 1 hour (actually 50 minutes)
Location
Skiles 246
Speaker
Longmei Shu – GT Math
Isospectral reductions on graphs remove certain nodes and change the weights of remaining edges. They preserve the eigenvalues of the adjacency matrix of the graph, their algebraic multiplicities and geometric multiplicities. They also preserve the eigenvectors. We call the graphs that can be isospectrally reduced to one same graph spectrally equivalent. I will give examples to show that two graphs can be spectrally equivalent or not based on the feature one picks for the equivalence class.

Stationary coalescing walks on the lattice

Series
Stochastics Seminar
Time
Thursday, February 21, 2019 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Arjun Krishnan – University of Rochester –
Consider a measurable dense family of semi-infinite nearest-neighbor paths on the integer lattice in d dimensions. If the measure on the paths is translation invariant, we completely classify their collective behavior in d=2 under mild assumptions. We use our theory to classify the behavior of families of semi-infinite geodesics in first- and last-passage percolation that come from Busemann functions. For d>=2, we describe the behavior of bi-infinite trajectories, and show that they carry an invariant measure. We also construct several examples displaying unexpected behavior. One of these examples lets us answer a question of C. Hoffman's from 2016. (joint work with Jon Chaika)

On Bounding the Number of Automorphisms of a Tournament

Series
Graph Theory Working Seminar
Time
Wednesday, February 20, 2019 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Michael Wigal – Georgia Tech
Let $g(n) = \max_{|T| = n}|\text{Aut}(T)|$ where $T$ is a tournament. Goldberg and Moon conjectured that $g(n) \le \sqrt{3}^{n-1}$ for all $n \ge 1$ with equality holding if and only if $n$ is a power of 3. Dixon proved the conjecture using the Feit-Thompson theorem. Alspach later gave a purely combinatorial proof. We discuss Alspach's proof and and some of its applications.

Minimal gaussian partitions with applications

Series
High Dimensional Seminar
Time
Wednesday, February 20, 2019 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Steven Heilman – USC

A single soap bubble has a spherical shape since it minimizes its surface area subject to a fixed enclosed volume of air. When two soap bubbles collide, they form a “double-bubble” composed of three spherical caps. The double-bubble minimizes total surface area among all sets enclosing two fixed volumes. This was proven mathematically in a landmark result by Hutchings-Morgan-Ritore-Ros and Reichardt using the calculus of variations in the early 2000s. The analogous case of three or more Euclidean sets is considered difficult if not impossible. However, if we replace Lebesgue measure in these problems with the Gaussian measure, then recent work of myself (for 3 sets) and of Milman-Neeman (for any number of sets) can actually solve these problems. We also use the calculus of variations. Time permitting, we will discuss an improvement to the Milman-Neeman result and applications to optimal clustering of data and to designing elections that are resilient to hacking. http://arxiv.org/abs/1901.03934

The symmetric Gaussian isoperimetric inequality

Series
Analysis Seminar
Time
Wednesday, February 20, 2019 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Steven Heilman – USC
It is well known that a Euclidean set of fixed Euclidean volume with least Euclidean surface area is a ball. For applications to theoretical computer science and social choice, an analogue of this statement for the Gaussian density is most relevant. In such a setting, a Euclidean set with fixed Gaussian volume and least Gaussian surface area is a half space, i.e. the set of points lying on one side of a hyperplane. This statement is called the Gaussian Isoperimetric Inequality. In the Gaussian Isoperimetric Inequality, if we restrict to sets that are symmetric (A= -A), then the half space is eliminated from consideration. It was conjectured by Barthe in 2001 that round cylinders (or their complements) have smallest Gaussian surface area among symmetric sets of fixed Gaussian volume. We discuss our result that says this conjecture is true if an integral of the curvature of the boundary of the set is not close to 1. https://arxiv.org/abs/1705.06643 http://arxiv.org/abs/1901.03934

AWM Lunch Talk Series - Anna Kirkpatrick: Markov Chain Monte Carlo and RNA Secondary Structure

Series
Other Talks
Time
Wednesday, February 20, 2019 - 12:00 for 30 minutes
Location
005
Speaker
Anna Kirkpatrick – Georgia Tech –
Understanding the structure of RNA is a problem of significant interest to biochemists. Thermodynamic energy functions are often key to this pursuit, but it is well-established that these energy functions do not perform well when applied to longer RNA sequences. This work specifically investigates the branching properties of RNA secondary structures, viewed as plane trees. By employing Markov chain Monte Carlo techniques, we sample from the probability distributions determined by these thermodynamic energy functions. We also investigate some of the challenges in employing Markov chain Monte Carlo, in particular the existence of local energy minima in transition graphs. This talk will give background, share preliminary results, and discuss future avenues of investigation.

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