Upcoming Seminars

Title: Joint Athens-Atlanta Number Theory Seminar
Seminar: Algebra
Speaker: Jiuya Wang and Andrew Obus of University of Georgia and The City University of New York
Contact: Andrew Kobin, andrew.jon.kobin@emory.edu
Date: 2024-04-16 at 4:00PM
Venue: Atwood 240
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Abstract:

Title: Quantifying the geometry of immune response and infection
Seminar: Numerical Analysis and Scientific Computing
Speaker: Manuchehr Aminian of Cal Poly Pomona
Contact: Manuela Girotti, manuela.girotti@emory.edu
Date: 2024-04-18 at 10:00AM
Venue: MSC W201
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Abstract: In improving outcomes for infection in humans and animals, it is important to understand how the body responds to an infection, whether infection has happened at all, and how this varies from individual to individual. Traditionally, this is a simple measurement -- does someone have a fever or not? With more precise, high-frequency measurements of macro-scale data (e.g. body temperature time series) and micro-scale data (e.g. protein or RNA data from biological samples, i.e. "omics"), we can develop and study the efficacy of more sophisticated algorithms and diagnostics. I will present past and ongoing work in applying ideas from geometrical data analysis and machine learning which aid us in making predictions in classification questions such as early prediction of infection, model-free learning of time series patterns and anomaly detection, and "inverse" problems such as prediction of time since infection. We will introduce algorithmic ideas to newcomers as well as our quantitative results on data coming from clinical studies with humans challenged with influenza-like illnesses, and Collaborative Cross mice studies, in work with our collaborators at Colorado State University and Texas A&M University.

Title: Reduced Unitary Whitehead Groups over Function Fields of $p$-adic Curves
Defense: Dissertation
Speaker: Zitong Pei of Emory Unviersity
Contact: Zitong Pei, zitong.pei@emory.edu
Date: 2024-04-22 at 11:00AM
Venue: MSC E406
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Abstract: The study of the Whitehead group of semi-simple simply connected groups is classical with an abundance of new open questions concerning the triviality of these groups. The Kneser-Tits conjecture on the triviality of these groups was answered in the negative by Platanov for general fields. There is a relation between reduced Whitehead groups and $R$-equivalence classes in algebraic groups.\\ \\ Let $G$ be an algebraic group over a field $F$. The $R$-equivalence, defined by Manin, is the equivalence relation on $G(F)$ defined by $x\sim y$ for $x, y \in G(F)$ if there exists a $F$-rational morphism ${\mathbb A}^1_K \cdots \to G$ defined at $0$ and $1$ and sending 0 to $x$ and 1 to $y$. Let $RG(F)$ be the equivalence class of the identity element in $G(F)$. Then $RG(F)$ is a normal subgroup of $G(F)$ and the quotient $G(F)/RG(F)$ is called the group of $R$-equivalence classes of $G(F)$. It is well known that for the semi-simple simply connected isotropic group $G$ over $F$, $W(G, F)$ is isomorphic to the group of $R$-equivalence classes. Thus the group of $R$-equivalence classes can be thought as Whitehead groups for general algebraic groups. The group of $R$-equivalence classes, is very useful while studying the rationality problem for algebraic groups, the problem to determine whether the variety of an algebraic group is rational or stably rational.\\ \\ Suppose that $D_0$ is a central division $F_0$-algebra. If the group $G(F_0)$ of rational points is given by $SL_n(D)$ for some $n>1$, then $W(G, F_0) $ is the reduced Whitehead group of $D_0$. Let $F$ be a quadratic field extension of $F_0$ and $D$ be a central division $F$-algebra. Suppose that $D$ has an involution of second kind $\tau$ such that $F^{\tau}=F_0$. If the hermitian form $h_{\tau}$ induced by $\tau$ is isotropic and the group $G(F_0)$ is given by $SU(h_\tau, D)$, then $W(G, F_0)$ is isomorphic to the reduced unitary Whitehead group of $D.$\\ \\ We start from the fundamental facts on reduced unitary Whitehead groups of central simple algebras, then introduce the patching techniques. Finally, let $F/F_0$ be a quadratic field extension of the function field of a $p$-adic curve. Let $A$ be a central simple algebra over $F$. Assume that the period of $A$ is two and $A$ has a unitary $F/F_0$ involution. We provide a proof for the triviality of the reduced unitary Whitehead group of $A$.

Title: Bayesian Modeling and Computation for Structural and Functional Neuroimaging
Seminar: Numerical Analysis and Scientific Computing
Speaker: Andrew Brown of Clemson University
Contact: Deepanshu Verma and Julianne Chung, deepanshu.verma@emory.edu
Date: 2024-04-25 at 10:00AM
Venue: MSC W201
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Abstract: Since its advent about 30 years ago, magnetic resonance imaging (MRI) has revolutionized medical imaging due to its ability to produce high-contrast images non-invasively without the use of radiation or injection. In neuroimaging in particular, MRI has become a very popular and useful tool both in clinical settings (e.g., in vivo measurements of anatomical structures) as well as psychology (e.g., studying neuronal activations over time in response to an external stimulus). Despite the applicability and history of MR-based neuroimaging, however, considerable challenges remain in the analysis of the associated data. In this talk, I will discuss two recent projects in which collaborators and I use fully Bayesian statistical modeling to draw inference about both brain structure and brain function. The former work illustrates how prior information can be used to improve our ability to delineate the hippocampus in patients with Alzheimer’s disease. The latter work discusses an approach that makes use of the full complex-valued data produced by an MR scanner to improve our ability to not only identify task-related activation in functional MRI, but to differentiate between types of activation that might carry different biological meaning. Along the way, I will mention some computational techniques we employ to facilitate Markov chain Monte Carlo (MCMC) algorithms to approximate the posterior distributions of interest.