## Seminars and Colloquia by Series

### Alice in Königsberg

Series
Other Talks
Time
Thursday, October 22, 2020 - 20:00 for 30 minutes
Location
ONLINE at https://zoom.us/j/93502013825
Speaker
Evans Harrell and GT Club Math studentsGeorgia Tech

This skit recounts one of the foundation stories of mathematics, the puzzle of the Seven Bridges of Königsberg, solved by Euler in 1726.  Except that it all takes place in a mad courtroom, and you are the jury!

### Higher-order fluctuations in dense random graph models (note the unusual time/day)

Series
Combinatorics Seminar
Time
Thursday, October 22, 2020 - 17:00 for 1 hour (actually 50 minutes)
Location
Speaker

Dense graph limit theory is essentially a first-order limit theory analogous to the classical Law of Large Numbers. Is there a corresponding central limit theorem? We believe so. Using the language of Gaussian Hilbert Spaces and the comprehensive theory of generalised U-statistics developed by Svante Janson in the 90s, we identify a collection of Gaussian measures (aka white noise processes) that describes the fluctuations of all orders of magnitude for a broad family of random graphs. We complement the theory with error bounds using a new variant of Stein’s method for multivariate normal approximation, which allows us to also generalise Janson’s theory in some important aspects. This is joint work with Gursharn Kaur.

### Higher-order fluctuations in dense random graph models (note the unusual time: 5pm)

Series
Stochastics Seminar
Time
Thursday, October 22, 2020 - 17:00 for 1 hour (actually 50 minutes)
Location
Speaker

Dense graph limit theory is essentially a first-order limit theory analogous to the classical Law of Large Numbers. Is there a corresponding central limit theorem? We believe so. Using the language of Gaussian Hilbert Spaces and the comprehensive theory of generalised U-statistics developed by Svante Janson in the 90s, we identify a collection of Gaussian measures (aka white noise processes) that describes the fluctuations of all orders of magnitude for a broad family of random graphs. We complement the theory with error bounds using a new variant of Stein’s method for multivariate normal approximation, which allows us to also generalise Janson’s theory in some important aspects. This is joint work with Gursharn Kaur.

Please note the unusual time: 5pm

### Generalized sum-product phenomena and a related coloring problem

Series
Graph Theory Seminar
Time
Tuesday, October 20, 2020 - 15:45 for 1 hour (actually 50 minutes)
Location
Speaker
Yifan JingUniversity of Illinois at Urbana-Champaign

In the first part of the talk, I will show that for two bivariate polynomials $P(x,y)$ and $Q(x,y)$ with coefficients in fields with char 0 to simultaneously exhibit small expansion, they must exploit the underlying additive or multiplicative structure of the field in nearly identical fashion. This in particular generalizes the main result of Shen and yields an Elekes-Ronyai type structural result for symmetric nonexpanders, resolving a question mentioned by de Zeeuw (Joint with S. Roy and C-M. Tran). In the second part of the talk, I will show how this sum-product phenomena helps us avoid color-isomorphic even cycles in proper edge colorings of complete graphs (Joint with G. Ge, Z. Xu, and T. Zhang).

### Quantitative stability for minimizing Yamabe metrics

Series
Analysis Seminar
Time
Tuesday, October 20, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
https://us02web.zoom.us/j/71579248210?pwd=d2VPck1CbjltZStURWRWUUgwTFVLZz09
Speaker
Robin NeumayerNorthwestern University

The Yamabe problem asks whether, given a closed Riemannian manifold, one can find a conformal metric of constant scalar curvature (CSC). An affirmative answer was given by Schoen in 1984, following contributions from Yamabe, Trudinger, and Aubin, by establishing the existence of a function that minimizes the so-called Yamabe energy functional; the minimizing function corresponds to the conformal factor of the CSC metric.

We address the quantitative stability of minimizing Yamabe metrics. On any closed Riemannian manifold we show—in a quantitative sense—that if a function nearly minimizes the Yamabe energy, then the corresponding conformal metric is close to a CSC metric. Generically, this closeness is controlled quadratically by the Yamabe energy deficit. However, we construct an example demonstrating that this quadratic estimate is false in the general. This is joint work with Max Engelstein and Luca Spolaor.

### Random Growth Models

Series
Time
Monday, October 19, 2020 - 15:30 for 1 hour (actually 50 minutes)
Location
Bluejeans meeting https://bluejeans.com/759112674
Speaker
Dr. Michael DamronGeorgia Tech

Random and irregular growth is all around us: tumor growth, fluid flow through porous media, and the spread of bacterial colonies. 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.

### On the Continuum Between Models, Data-Driven Discovery and Machine Learning: Mapping the Continuum of Molecular Conformations Using Cryo-Electron Microscopy

Series
Applied and Computational Mathematics Seminar
Time
Monday, October 19, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/884917410
Speaker
Roy Lederman Yale University

Cryo-Electron Microscopy (cryo-EM) is an imaging technology that is revolutionizing structural biology. Cryo-electron microscopes produce a large number of very noisy two-dimensional projection images of individual frozen molecules; unlike related methods, such as computed tomography (CT), the viewing direction of each particle image is unknown. The unknown directions, together with extreme levels of noise and additional technical factors, make the determination of the structure of molecules challenging. While other methods for structure determination, such as x-ray crystallography and nuclear magnetic resonance (NMR), measure ensembles of molecules, cryo-electron microscopes produce images of individual molecules. Therefore, cryo-EM could potentially be used to study mixtures of different conformations of molecules. Indeed, current algorithms have been very successful at analyzing homogeneous samples, and can recover some distinct conformations mixed in solutions, but, the determination of multiple conformations, and in particular, continuums of similar conformations (continuous heterogeneity), remains one of the open problems in cryo-EM. In practice, some of the key components in “molecular machines” are flexible and therefore appear as very blurry regions in 3-D reconstructions of macro-molecular structures that are otherwise stunning in resolution and detail.

We will discuss “hyper-molecules,” the mathematical formulation of heterogenous 3-D objects as higher dimensional objects, and the machinery that goes into recovering these “hyper-objects” from data. We will discuss some of the statistical and computational challenges, and how they are addressed by merging data-driven exploration, models and computational tools originally built for deep-learning.

This is joint work with Joakim Andén and Amit Singer.

### Ribbon homology cobordism

Series
Geometry Topology Seminar
Time
Monday, October 19, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Speaker
Shea Vela VickLouisiana State University

A cobordism between 3-manifolds is ribbon if it is built from handles of index no greater than 2. Such cobordisms arise naturally from several different topological and geometric contexts. In this talk, we discuss these objects and present a few obstructions to their existence, from Thurston geometries, character varieties, and instanton and Heegaard Floer homologies. This is joint work with Aliakbar Daemi, Tye Lidman, and Mike Wong.

### Symmetries of Surfaces

Series
Research Horizons Seminar
Time
Friday, October 16, 2020 - 12:30 for 1 hour (actually 50 minutes)
Location
Microsoft Teams
Speaker
Marissa LovingGeorgia Tech

There are many ways to study surfaces: topologically, geometrically, dynamically, algebraically, and combinatorially, just to name a few. We will touch on some of the motivation for studying surfaces and their associated mapping class groups, which is the collection of symmetries of a surface. We will also describe a few of the ways that these different perspectives for studying surfaces come together in beautiful ways.

### Toppleable Permutations, Ursell Functions and Excedances

Series
Combinatorics Seminar
Time
Friday, October 16, 2020 - 10:00 for 1 hour (actually 50 minutes)
Location
Speaker
Arvind AyyerIndian Institute of Science, Bengaluru, India

Recall that an excedance of a permutation $\pi$ is any position $i$
such that $\pi_i > i$. Inspired by the work of Hopkins, McConville and
Propp (arXiv:1612.06816) on sorting using toppling, we say that
a permutation is toppleable if it gets sorted by a certain sequence of
toppling moves. For the most part of the talk, we will explain the
main ideas in showing that the number of toppleable permutations on n
letters is the same as those for which excedances happen exactly at
$\{1,\dots, \lfloor (n-1)/2 \rfloor\}$. Time permitting, we will give
some ideas showing that this is also the number of acyclic
orientations with unique sink (also known as the Ursell function) of the
complete bipartite graph $K_{\lceil n/2 \rceil, \lfloor n/2 \rfloor + 1}$.

This is joint work with D. Hathcock (CMU) and P. Tetali (Georgia Tech).