All Seminars
| Title: Mathematical Modeling and Numerical Simulation of the Heart Function Speaker's Name: Alfio Quarteroni |
|---|
| Seminar: CODES |
| Speaker: Alfio Quarteroni of Politecnico Milano and EPFL |
| Contact: Alessandro Veneziani, avenez2@emory.edu |
| Date: 2025-04-18 at 3:30PM |
| Venue: Oxford Building Room 311 |
| Download Flyer |
| Abstract: Computational medicine is a powerful driver of mathematical innovation, generating complex problems and numerical methods that enhance our understanding of human physiology. It also provides invaluable support to physicians, enabling more accurate diagnoses, optimized therapies, and patient-specific surgical interventions. However, the challenges posed by the multiphysics and multiscale nature of these problems—combined with data uncertainty, inter- and intra-patient variability, and the curse of dimensionality—are significant. In this presentation, we will demonstrate how the iHEART simulator—a comprehensive model of human heart function, combining physics-based computational modeling with data-driven algorithms—enables us to overcome these challenges and achieve these objectives. |
| Title: Brauer groups of stacky curves |
|---|
| Seminar: Algebra and Number Theory |
| Speaker: Niven Achenjang of MIT |
| Contact: TBA |
| Date: 2025-04-08 at 4:00PM |
| Venue: MSC W303 |
| Download Flyer |
| Abstract: Brauer groups $\mathrm{Br}(-) = H^2(-, \mathbb{G}_m)$ can be used to define obstructions to points on varieties (supersets of a variety’s set of points). Notably, Harari and Voloch have conjectured that the integral Brauer-Manin obstruction on a (hyperbolic, affine) rational curve exactly cuts out its set of integral points. Given this, one might wonder about the efficacy of applying Brauer-Manin obstructions to (hyperbolic) stacky rational curves, such as the moduli space $\mathscr Y(1)$ of elliptic curves; however, one would first need to understand the Brauer groups of such stacky curves! In this talk, I will discuss some general technical results for computing Brauer groups of stacky curves and highlight their usefulness via the example of computing the Brauer group of $\mathscr Y(1)$, over a fairly general base $S$ (e.g. $S =\mathbb Q,\mathbb Z[1/2]$, or a curve over a finite field). |
| Title: 17T7 is a Galois group over the rationals |
|---|
| Seminar: Algebra |
| Speaker: John Voight of University of Sydney |
| Contact: Santiago Arango, santiago.arango@emory.edu |
| Date: 2025-04-04 at 3:00PM |
| Venue: MSC W301 |
| Download Flyer |
| Abstract: We prove that the transitive permutation group 17T7 is a Galois group over the rationals, completing the list of transitive subgroups ordered by degree up to 23 (leaving the Mathieu group on 23 letters as the next missing group). We exhibit such a Galois extension using methods from arithmetic geometry. This is joint work with Raymond van Bommel, Edgar Costa, Noam Elkies, Timo Keller, and Sam Schiavone. |
| Title: Low-degree points on some rank 0 modular curves |
|---|
| Defense: Dissertation |
| Speaker: Alexis Newton of |
| Contact: Alexis Newton, alexis.newton@emory.edu |
| Date: 2025-03-27 at 4:00PM |
| Venue: MSC N306 |
| Download Flyer |
| Abstract: Let $E$ be an elliptic curve defined over a number field $K$. We present some new progress on the classification of the finite groups which appear as the torsion subgroup of $E(K)$ as $K$ ranges over quartic, quintic and sextic number fields. In particular, we concentrate on determining the quartic, quintic and sextic points on certain modular curves $X_1(N)$ for which the rank of $J_0(N)$ is zero. |
| Title: Independent Sets in H-free Hypergraphs |
|---|
| Seminar: Combinatorics |
| Speaker: Xiaoyu He, PhD of Georgia Institute of Technology |
| Contact: Dr. Cosmin Pohoata, apohoat@emory.edu |
| Date: 2025-03-26 at 11:00AM |
| Venue: MSC W201 |
| Download Flyer |
| Abstract: It is a fundamental question in Ramsey theory to determine the smallest possible independence number of an H-free hypergraph on n vertices. In the case of graphs, the problem was famously solved for H=K3 by Kim and for H=K4 (up to a logarithmic factor) by Mattheus-Verstraete in 2023. Even C4 and K5 remain wide open. We study the problem for 3-uniform hypergraphs and conjecture a full classification: the minimum independence number is poly(n) if and only if H is contained in the iterated blowup of the single-edge hypergraph. We prove this conjecture for all H with at most two tightly connected components. Based on joint work with Conlon, Fox, Gunby, Mubayi, Suk, Verstraete, and Yu. |
| Title: From Uncertainty Aware to Decision Ready: Specialized UQ Methods for High-Stakes Predictive Modeling |
|---|
| Defense: Dissertation |
| Speaker: Shifan Zhao of |
| Contact: Shifan Zhao, shifan.zhao@emory.edu |
| Date: 2025-03-26 at 11:30AM |
| Venue: MSC E406 |
| Download Flyer |
| Abstract: Uncertainty quantification (UQ) is essential for reliable decision-making in predictive modeling, particularly those with high-stakes outcomes. This thesis develops a unified framework that tailors uncertainty quantification methods to AI foundation models with distinct application domains. For stationary foundation models, we enhance traditional Gaussian Process regression—through kernel preconditioning and a two-stage modeling approach—to address computational inefficiencies, approximation bias, and model misspecification, thereby improving uncertainty estimates. For nonstationary foundation models, we integrate conformal prediction techniques to exploit theoretical guarantees of data coverage. We apply our methods to medical and climate foundations models, and numerical experiments demonstrate that our targeted approaches produce reliable and actionable estimates of uncertainty. This work shows the potential to substantially advance the state of predictive modeling for both healthcare and extreme weather applications. |
| Title: Convergent Decomposition Groups and an S-adic Shafarevich Conjecture |
|---|
| Seminar: Algebra |
| Speaker: Andrew Kwon of University of Pennsylvania |
| Contact: Deependra Singh, deependra.singh@emory.edu |
| Date: 2025-03-25 at 4:00PM |
| Venue: MSC W303 |
| Download Flyer |
| Abstract: Local-global principles for rational points have a long and influential role in arithmetic geometry. Our focus will be on what a universal local-global principle for rational points implies about the Galois theory of the field, especially fields of totally S-adic numbers, where S is an infinite set of places. Some applications of our work include: (i) new evidence for the Shafarevich Conjecture on the freeness of the absolute Galois group of the maximal cyclotomic extension of k; (ii) "independence" of the decomposition groups above infinite families of primes. Time permitting, we will also mention several areas for future work. |
| Title: Scattering phase shifts on asymptotically hyperbolic manifolds |
|---|
| Seminar: Analysis and PDE |
| Speaker: Antonio Sa Barreto of Purdue University |
| Contact: Yiran Wang, yiran.wang@emory.edu |
| Date: 2025-03-21 at 11:00AM |
| Venue: MSC W301 |
| Download Flyer |
| Abstract: When a wave interacts with a perturbation it undergoes a phase shift, and one can observe this even for second order differential equations of one variable. This phenomenon has been well studied by physicists and mathematicians, (as far as I know) starting from the 1930’s, largely for perturbations of the Euclidean Laplacian by real valued radially symmetric potentials. In the 1980’s Birman and Yafaev studied the distribution of phase shifts for certain non-central potentials in Euclidean space for fixed energy. This was followed by the work of Bulger and Pushnitski in 2012 for the high energy limit still in Euclidean space. Nakamura studied the problem for fixed energies, but on manifolds. Datchev, Gell-Redmann, Hassell, Ingremeau, Zelditch and others studied the semiclassical problem, but still for perturbations of the Euclidean space. We discuss the high energy limit for potential perturbations of the hyperbolic space and more generally on (non-trapping) asymptotically hyperbolic manifolds. We also discuss the inverse problem of determining a potential from the high energy limit of scattering shifts. |
| Title: Random feature expansions guided by input weighting |
|---|
| Seminar: CODES |
| Speaker: John Darges of Emory University |
| Contact: Levon Nurbekyan, lnurbek@emory.edu |
| Date: 2025-03-20 at 10:00AM |
| Venue: MSC W301 |
| Download Flyer |
| Abstract: Random feature expansions (RFEs) approximate functions by as an expansion of random selections of basis functions from a specific class. The approach emerged from both neural networks and from random feature approximations to kernel matrices. Popular formulations like random Fourier expansions connect these two areas. Recent work advocates using RFEs, as surrogate models to emulate multivariable functions, for applications in uncertainty quantification. In this talk, we put forth an advancement in RFE-based surrogate modeling. Our proposed algorithm learns underlying input interaction structure in the target model and builds this into the RFE surrogate. We give insight into the method via theoretical underpinnings--reproducing kernels, feature maps, and decompositions of multivariable functions--and by presenting its performance in numerical experiments |
| Title: Rationality of Brauer-Severi surface bundles over rational 3-folds |
|---|
| Seminar: Algebra and Number Theory |
| Speaker: Shitan Xu of Michigan State University |
| Contact: Deependra Singh, deependra.singh@emory.edu |
| Date: 2025-03-04 at 4:00PM |
| Venue: MSC W303 |
| Download Flyer |
| Abstract: Rationality problems for conic bundles have been well studied over surfaces. In this talk, we generalize an etale cohomology diagram from the case of conic bundles to Brauer-Severi surface bundles over rational 3-folds . We use this generalization to prove a sufficient condition for a Brauer-Severi surface bundle to be not stably Rational. We also give an example satisfying these sufficient conditions. |