Seminars and Colloquia by Series

Matrix superconcentration inequalities

Series
Stochastics Seminar
Time
Thursday, March 13, 2025 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Tatiana BrailovskayaDuke University

One way to understand the concentration of the norm of a random matrix X with Gaussian entries is to apply a standard concentration inequality, such as the one for Lipschitz functions of i.i.d. standard Gaussian variables, which yields subgaussian tail bounds on the norm of X. However, as was shown by Tracy and Widom in 1990s, when the entries of X are i.i.d. the norm of X exhibits even sharper concentration. The phenomenon of a function of many i.i.d. variables having strictly smaller tails than those predicted by classical concentration inequalities is sometimes referred to as «superconcentration», a term originally dubbed by Chatterjee. I will discuss novel results that can be interpreted as superconcentration inequalities for the norm of X, where X is a Gaussian random matrix with independent entries and an arbitrary variance profile. We can also view our results as a nonhomogeneous extension of Tracy-Widom-type upper tail estimates for the norm of X.

Theory of valuations and geometric inequalities

Series
School of Mathematics Colloquium
Time
Thursday, March 13, 2025 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Semyon AleskerTel Aviv University and Kent State University

Valuations are finitely additive measures on convex compact sets. In the last two decades a number of structures (e.g. product and convolution)  with non-trivial properties were discovered on the space of valuations. One such recently discovered property is an analogue of the classical Hodge-Riemann bilinear relations known in algebraic/Kaehler geometry. In special cases, they lead to new inequalities for convex bodies, to be discussed in the talk. No familiarity with valuations theory and algebraic/Kaehler geometry is assumed.

VC dimension and point configurations in fractals

Series
Analysis Seminar
Time
Wednesday, March 12, 2025 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Alexander McDonaldKennesaw State

An important class of problems at the intersection of harmonic analysis and geometric measure theory asks how large the Hausdorff dimension of a set must be to ensure that it contains certain types of geometric point configurations. We apply these tools to study configurations associated to the problem of bounding the VC-dimension of a naturally arising class of indicator functions on fractal sets.

Tight minimum colored degree condition for rainbow connectivity

Series
Graph Theory Seminar
Time
Tuesday, March 11, 2025 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Xiaofan YuanArizona State University

Let $G = (V,E)$ be a graph on $n$ vertices, and let $c : E \to P$, where $P$ is a set of colors. Let $\delta^c(G) = \min_{v \in V} \{ d^{c}(v) \}$ where $d^c(v)$ is the number of colors on edges incident to a vertex $v$ of $G$.  In 2011, Fujita and Magnant showed that if $G$ is a graph on $n$ vertices that satisfies $\delta^c(G)\geq n/2$, then for every two vertices $u, v$ there is a properly-colored $u,v$-path in $G$. We show that for sufficiently large graphs $G$ the same bound for $\delta^c(G)$ implies that any two vertices are connected by a rainbow path. This is joint work with Andrzej Czygrinow.

Vanishing cycles and almost toric fibrations by Jie Min

Series
Geometry Topology Seminar
Time
Monday, March 10, 2025 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jie MinUniversity of Massachusetts Amherst

Vanishing cycles of Lefschetz fibrations give examples of Lagrangian spheres in the fiber. A natural question, first raised by Donaldson, is whether all Lagrangian spheres arise this way. We focus on this problem for positive rational surfaces, which were shown to admit a geometric structure called almost toric fibrations. I will talk about a work-in-progress showing all Lagrangian spheres here are visible in an almost toric fibration and thus are vanishing cycles of a nodal degeneration.

From Theory to Practice: Mathematical Approaches to Scientific Machine Learning

Series
Applied and Computational Mathematics Seminar
Time
Monday, March 10, 2025 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005 and https://gatech.zoom.us/j/94954654170
Speaker
Yeonjong ShinNCSU

Machine learning (ML) has achieved unprecedented empirical success in diverse applications. It now has been applied to solve scientific and engineering problems, which has become an emerging field, Scientific Machine Learning (SciML). However, many ML techniques are highly complex and sophisticated, often requiring extensive trial-and-error experimentation and specialized problem-dependent tricks to implement effectively. This complexity frequently leads to significant challenges, such as reproducibility and rigorness, for scientific research. This talk explores mathematical approaches, offering more principled and reliable methodologies in SciML. The first part will present recent efforts advancing the predictive power of physics-informed machine learning through robust training/optimization methods. This includes an effective training method for multivariate neural networks, namely, Active Neuron Least Squares (ANLS) and a two-step training method for deep operator networks. The second part is about how to embed the first principles of physics into neural networks. I will present a general framework for designing NNs that obey the first and second laws of thermodynamics. The framework not only provides flexible ways of leveraging available physics information but also results in expressive NN architectures. I will also present an intriguing phenomenon of this framework when it is applied in the context of latent space dynamics identification where a correlation appears between an entropy production rate in the latent space and the behaviors of the full-state solution.

Forbidden Minor Results for Flag Matroids

Series
Algebra Seminar
Time
Monday, March 10, 2025 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Nathaniel VaduthalaTulane University

Please Note: There will be a pre-seminar from 10:55 to 11:15 in Skiles 005.

Similar to how matroids can be viewed as a combinatorial abstraction of linear subspaces, a flag matroid can be viewed as a combinatorial abstraction of a nested sequence of linear subspaces. In this talk, we will discuss forbidden minor results that describe precisely when a flag matroid is representable and when it is graphic. 

Mathapalooza!

Series
Other Talks
Time
Sunday, March 9, 2025 - 15:00 for 4 hours (half day)
Location
Sun ATL Gallery, 399 Edgewood Ave SE, Atlanta, GA 30312
Speaker
Many

Please Note: Mathapalooza! is a math-themed event at the Atlanta Science Festival. If you want to volunteer to help on March 9, please write to Evans Harrell

The 2025 Atlanta Science Festival Mathapalooza! will take place in an art gallery at the opening of an exhibition, The Art of Math.  The show will begin with magic by Matt Baker, followed by hands-on art construction, circus acts, "Math Court" skits, and 4-dimensional dance, before ending with a performance by Tracy Woodard of Bach's Crab Canon, with a discussion of its symmetry algebra.  Find out more and get tickets at https://atlantasciencefestival.org/events-2025/1113-mathapalooza-at-the-gallery/

On the original Ulam's problem and its quantization

Series
CDSNS Colloquium
Time
Friday, March 7, 2025 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 314
Speaker
Jing ZhouGreat Bay University (Dongguan)

Please Note: Zoom link: https://gatech.zoom.us/j/91390791493?pwd=QnpaWHNEOHZTVXlZSXFkYTJ0b0Q0UT09

In 1961 Ulam proposed a mathematical simplification extracting the essential accelerating mechanism proposed by Fermi, as to explain the cause of high-energy particles in cosmic rays. In this talk, we shall describe the typical behavior of the very model introduced by Ulam in both the classical original form as well as its quantization. In the classical model, we show that typical orbits are recurrent under resonance assumptions. Meanwhile in the quantum model, the acceleration caused by resonance gets much amplified and we point out a direct relationship between the acceleration behavior of the system and the shape of its quasi-energy spectrum. This is a joint work in progress with Changguang Dong and Disheng Xu.

Unsupervised Solution Operator Learning for Mean-Field Games

Series
Applied and Computational Mathematics Seminar
Time
Friday, March 7, 2025 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006 and https://gatech.zoom.us/j/98355006347
Speaker
Rongjie LaiPurdue University

Recent advances in deep learning have introduced numerous innovative frameworks for solving high-dimensional mean-field games (MFGs). However, these methods are often limited to solving single-instance MFGs and require extensive computational time for each instance, presenting challenges for practical applications.

In this talk, I will present our recent work on a novel framework for learning the MFG solution operator. Our model takes MFG instances as input and directly outputs their solutions in a single forward pass, significantly improving computational efficiency. Our method offers two key advantages: (1) it is discretization-free, making it particularly effective for high-dimensional MFGs, and (2) it can be trained without requiring supervised labels, thereby reducing the computational burden of preparing training datasets common in existing operator learning methods. If time permits, I will also explore connections between this framework and in-context learning, highlighting its broader implications and potential for further advancements.

 

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