## Seminars and Colloquia by Series

### TBA by Ruth Luo

Series
Combinatorics Seminar
Time
Friday, October 14, 2022 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 202
Speaker
Ruth LuoUniversity of South Carolina

### Spectral Properties of Periodic Elastic Beam Hamiltonians on Hexagonal Lattices

Series
Math Physics Seminar
Time
Thursday, October 13, 2022 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles Room 005
Speaker
Burak HatinogluSchool of Mathematics, Georgia Tech

Elastic beam Hamiltonians on single-layer graphs are constructed out of Euler-Bernoulli beams, each governed by a scalar valued fourth-order Schrödinger operator equipped with a real symmetric potential. Unlike the second-order Schrödinger operator commonly applied in quantum graph literature, here the self-adjoint vertex conditions encode geometry of the graph by their dependence on angles at which edges are met. In this talk, I will first consider spectral properties of this Hamiltonian with periodic potentials on a special equal-angle lattice, known as graphene or honeycomb lattice. I will also discuss spectral properties for the same operator on lattices in the geometric neighborhood of graphene. This talk is based on a joint work with Mahmood Ettehad (University of Minnesota),https://arxiv.org/pdf/2110.05466.pdf.

### TBA by Dmitrii M. Ostrovskii

Series
Stochastics Seminar
Time
Thursday, October 13, 2022 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Dmitrii M. OstrovskiiUniversity of Southern California

### Learning to Solve Hard Minimal Problems

Series
School of Mathematics Colloquium
Time
Thursday, October 13, 2022 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Anton LeykinGeorgia Tech

The main result in this talk concerns a new fast algorithm to solve a minimal problem with many spurious solutions that arises as a relaxation of a geometric optimization problem. The algorithm recovers relative camera pose from points and lines in multiple views. Solvers like this are the backbone of structure-from-motion techniques that estimate 3D structures from 2D image sequences.

Our methodology is general and applicable in areas other than computer vision. The ingredients come from algebra, geometry, numerical methods, and applied statistics. Our fast implementation relies on a homotopy continuation optimized for our setting and a machine-learned neural network.

(This covers joint works with Tim Duff, Ricardo Fabbri, Petr Hruby, Kathlen Kohn, Tomas Pajdla, and others.

The talk is suitable for both professors and students.)

### Learning to Solve Hard Minimal Problems

Series
Colloquia
Time
Thursday, October 13, 2022 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Anton LeykinGeorgia Tech

The main result in this talk concerns a new fast algorithm to solve a minimal problem with many spurious solutions that arises as a relaxation of a geometric optimization problem. The algorithm recovers relative camera pose from points and lines in multiple views. Solvers like this are the backbone of structure-from-motion techniques that estimate 3D structures from 2D image sequences.

Our methodology is general and applicable in areas other than computer vision. The ingredients come from algebra, geometry, numerical methods, and applied statistics. Our fast implementation relies on a homotopy continuation optimized for our setting and a machine-learned neural network.

(This covers joint works with Tim Duff, Ricardo Fabbri, Petr Hruby, Kathlen Kohn, Tomas Pajdla, and others. The talk is suitable for both professors and students.)

### Bounds on some classical exponential Riesz basis

Series
Analysis Seminar
Time
Wednesday, October 12, 2022 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Thibaud AlemanyGeorgia Tech

We estimate the  Riesz basis (RB) bounds obtained in Hruschev, Nikolskii and Pavlov' s classical characterization of exponential RB. As an application, we  improve previously known estimates of the RB bounds in some classical cases, such as RB obtained by an Avdonin type perturbation, or RB which are the zero-set of sine-type functions. This talk is based on joint work with S. Nitzan

### TBA

Series
Geometry Topology Student Seminar
Time
Wednesday, October 12, 2022 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
TBA

TBA

### Random growth models

Series
Research Horizons Seminar
Time
Wednesday, October 12, 2022 - 12:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Michael DamronGeorgia Tech

Random and irregular growth is all around us. We see it in the form of cancer growth, bacterial infection, fluid flow through porous rock, and propagating flame fronts. Simple models for these processes originated in the '50s with percolation theory and have since given rise to many new models and interesting mathematics. I will introduce a few models (percolation, invasion percolation, first-passage percolation, diffusion-limited aggregation, ...), along with some of their basic properties.

### Progress towards the Burning Number Conjecture

Series
Graph Theory Seminar
Time
Tuesday, October 11, 2022 - 15:45 for 1 hour (actually 50 minutes)
Location
Speaker
Jérémie TurcotteMcGill University

The burning number $b(G)$ of a graph $G$ is the smallest integer $k$ such that $G$ can be covered by $k$ balls of radii respectively $0,\dots,k-1$, and was introduced independently by Brandenburg and Scott at Intel as a transmission problem on processors \cite{alon} and Bonato, Janssen and Roshanbin as a model for the spread of information in social networks.

The Burning Number Conjecture \cite{bonato} claims that $b(G)\leq \left\lceil\sqrt{n}\right\rceil$, where $n$ is the number of vertices of $G$. This bound tight for paths. The previous best bound for this problem, by Bastide et al. \cite{bastide}, was $b(G)\leq \sqrt{\frac{4n}{3}}+1$.

We prove that the Burning Number Conjecture holds asymptotically, that is $b(G)\leq (1+o(1))\sqrt{n}$.

Following a brief introduction to graph burning, this talk will focus on the general ideas behind the proof.

### Multi-scale modeling for complex flows at extreme computational scales

Series
Applied and Computational Mathematics Seminar
Time
Monday, October 10, 2022 - 14:00 for
Location
Skiles 005 and https://gatech.zoom.us/j/98355006347
Speaker
Spencer BryngelsonGeorgia Tech CSE

Many fluid flows display at a wide range of space and time scales. Turbulent and multiphase flows can include small eddies or particles, but likewise large advected features. This challenge makes some degree of multi-scale modeling or homogenization necessary. Such models are restricted, though: they should be numerically accurate, physically consistent, computationally expedient, and more. I present two tools crafted for this purpose. First, the fast macroscopic forcing method (Fast MFM), which is based on an elliptic pruning procedure that localizes solution operators and sparse matrix-vector sampling. We recover eddy-diffusivity operators with a convergence that beats the best spectral approximation (from the SVD), attenuating the cost of, for example, targeted RANS closures. I also present a moment-based method for closing multiphase flow equations. Buttressed by a recurrent neural network, it is numerically stable and achieves state-of-the-art accuracy. I close with a discussion of conducting these simulations near exascale. Our simulations scale ideally on the entirety of ORNL Summit's GPUs, though the HPC landscape continues to shift.