Upcoming Seminars

Title: About the Lp theory for the non-cutoff Boltzmann equation
Seminar: Analysis and Differential Geometry
Speaker: Ricardo Alonso of Texas A$\&$M at Qatar
Contact: Maja Taskovic, maja.taskovic@emory.edu
Date: 2022-09-29 at 4:00PM
Venue: MSC W301
Download Flyer
Abstract:
In this talk we discuss different technical elements to obtain a priori estimates for Lp norms of weak solutions to non-cutoff kinetic equations using as example the homogeneous/inhomogeneous Boltzmann equation. Rather than a detailed-proof talk, we point out difficulties and give some intuition related to the main steps of the strategy. In particular, we discuss the localization process of Boltzmann type operators which cover an ample range of operators such as the fractional Laplacian.
Title: Smooth limits of plane curves and Markov numbers
Seminar: Algebra
Speaker: David Stapleton of The University of Michigan
Contact: David Zureick-Brown, david.zureick-brown@emory.edu
Date: 2022-10-04 at 4:00PM
Venue: MSC N304
Download Flyer
Abstract:
When can we guarantee that smooth proper limits of plane curves are still plane curves? Said a different way --- When is the locus of degree d plane curves closed in the (open) moduli space of smooth genus g curves? It is relatively easy to see that if d>1, then d must be prime. Interestingly, this is not sufficient -- Griffin constructed explicit families of quintic plane curves with a smooth limit that is not a quintic plane curve. In this talk we propose the following conjecture: Smooth proper limits of plane curves of degree d are always planar if d is prime and d is not a Markov number. We discuss the motivation and evidence for this conjecture which come from Hacking and Prokhorov's work on Q-Gorenstein limits of the projective plane.
Title: Patch Normalizing Regularizer: Reconstruction using only one ground truth image
Seminar: Computational and Data Enabled Science
Speaker: Paul Hagemann of TU Berlin
Contact: Lars Ruthotto, lruthotto@emory.edu
Date: 2022-10-06 at 10:00AM
Venue: MSC W301
Download Flyer
Abstract:
Reconstructing images from measurements (e.g. sinograms in CT) is a very active research topic. However in many domains, such as medical or material sciences, ground truth data is very hard or costly to obtain. In this talk, we will leverage the idea of patch-based learning for reconstructing images. The regularizer will learn the patch distribution from very few ground truth images by randomly subsampling 6x6 patches and learning their distribution. More specifically, we will use a normalizing flow to learn the patch distribution of the ground truth image, which we call patchNR. In reconstruction, we will minimize a sum of the negative log likelihood of the patches and the data fidelity term. Our method will be compared to other regularization techniques which use little data for CT, material and texture images. Furthermore, an outlook on how our method can be leveraged to perform zero shot superresolution will be given.
Title: Complexities of the Cytoskeleton: Integration of Scales
Seminar: Computational and Data Enabled Science
Speaker: Keisha Cook of Clemson University
Contact: Jim Nagy, jnagy@emory.edu
Date: 2022-10-07 at 1:00PM
Venue: MSC W301
Download Flyer
Abstract:
Biological systems are traditionally studied as isolated processes (e.g. regulatory pathways, motor protein dynamics, transport of organelles, etc.). Although more recent approaches have been developed to study whole cell dynamics, integrating knowledge across biological levels remains largely unexplored. In experimental processes, we assume that the state of the system is unknown until we sample it. Many scales are necessary to quantify the dynamics of different processes. These may include a magnitude of measurements, multiple detection intensities, or variation in the magnitude of observations. The interconnection between scales, where events happening at one scale are directly influencing events occurring at other scales, can be accomplished using mathematical tools for integration to connect and predict complex biological outcomes. In this work we focus on building inference methods to study the complexity of the cytoskeleton from one scale to another.
Title: A Random Group with Local Data
Seminar: Algebra
Speaker: Brandon Alberts of Eastern Michigan University
Contact: David Zureick-Brown, david.zureick-brown@emory.edu
Date: 2022-10-14 at 4:00PM
Venue: MSC W301
Download Flyer
Abstract:
The Cohen--Lenstra heuristics describe the distribution of $\ell$-torsion in class groups of quadratic fields as corresponding to the distribution of certain random p-adic matrices. These ideas have been extended to using random groups to predict the distributions of more general unramified extensions in families of number fields (see work by Boston--Bush--Hajir, Liu--Wood, Liu--Wood--Zureick-Brown). Via the Galois correspondence, the distribution of unramified extensions is a specific example of counting number fields with prescribed ramification and bounded discriminant. As of yet, no constructions of random groups have been given in the literature to predict the answers to famous number field counting conjectures such as Malle's conjecture. We construct a "random group with local data" bridging this gap, and use it to describe new heuristic justifications for number field counting questions.
Title: TBA
Seminar: Algebra
Speaker: Soumya Sankar of The Ohio State University
Contact: David Zureick-Brwon, david.zureick-brown@emory.edu
Date: 2022-10-14 at 5:15PM
Venue: MSC W301
Download Flyer
Abstract:
Title: Subspace configurations and low degree points on curves
Seminar: Algebra
Speaker: Borys Kadets of University of Georgia
Contact: David Zureick-Brown, david.zureick-brown@emory.edu
Date: 2022-10-18 at 4:00PM
Venue: MSC N304
Download Flyer
Abstract:
The hyperelliptic curve given by the equation $y^2=f(x)$ with coefficients in $\mathbf{Q}$ has an unusual arithmetic property: it admits infinitely many points with coordinates in quadratic extensions of $\mathbf{Q}$ (namely $(a, \sqrt{f(a)})$). Hindry, motivated by arithmetic questions about modular curves, asked if the only curves that possess infinite collections of quadratic points are hyperelliptic and bielliptic; this conjecture was confirmed by Harris and Silverman. I will talk about the general problem of classifying curves that possess infinite collections of degree $d$ points. I will explain how to reduce this classification problem to a study of curves of low genus, and use this reduction to obtain a classification for $d \leq 5$. This relies on analyzing a discrete-geometric object -- the subspace configuration -- attached to curves with infinitely many degree $d$ points. This talk is based on joint work with Isabel Vogt (arXiv:2208.01067).
Title: TBA
Seminar: Algebra
Speaker: Daniel Keliher of University of Georgia
Contact: David Zureick-Brown, david.zureick-brown@emory.edu
Date: 2022-11-01 at 4:00PM
Venue: MSC N304
Download Flyer
Abstract:
Title: Athens-Atlanta joint Number Theory Seminar
Seminar: Algebra
Speaker: Alina Bucur and Samit Dasgupta of USCD and Duke
Contact: David Zureick-Brown, david.zureick-brown@emory.edu
Date: 2022-11-07 at 4:00PM
Venue: MSC W301
Download Flyer
Abstract: