### Seminars and Colloquiums for the week of December 2, 2019

SPEAKERS
Monday
Math Biology Seminar
Loannis Sgouralis, Postdoctoral Scholar, Center for Biological Physics at Arizona State University
Wednesday
Sui Tang, Postdoc Fellow, Johns Hopkins University
Dony Varghese, UTK
Thursday
Shuler Hopkins, UTK
Raquel Perales, National University of Mexico
Friday
Tamara Riggs, UTK
Wei Zhu, Duke University

Monday, Nov. 2

MATH BIOLOGY SEMINAR
TITLE: Sharing of videos for the various seminar topics by participants.
TIME: 10:10 AM -11:00AM
ROOM: Claxton 105

COLLOQUIUM
TITLE: Data-driven modeling and interpretation in Biophysics and Chemistry
SPEAKER: Loannis Sgouralis, Postdoctoral Scholar, Center for Biological Physics at Arizona State University
TIME: 3:30 PM-4:30 PM
ROOM: Ayres 405
Abstract: Modern experiments monitor physical systems with high resolution that may reach the molecular level. Excessive noise caused by the measuring hardware and the experimental procedures or unaccounted processes demand the formulation of specialized methods for the analysis and interpretation of the acquired datasets. Nevertheless, physical limitations and the inherent uncertainties in the underlying systems, such as unknown parameters, states, or dynamics pose unique conceptual and computational challenges that lead to intractable model selection problems. In this talk, I will present an overview on the difficulties that are commonly encountered. I will also highlight recent advances, including novel Bayesian non-parametric approaches, which provide elegant alternatives to model selection.

Wednesday, Nov. 4

COLLOQUIUM

TITLE: Learning interaction kernels in agent-based systems
SPEAKER: Sui Tang, Postdoc Fellow, Johns Hopkins University
TIME: 3:35 PM
ROOM: Ayres 405
Abstract:  Agent-based systems are ubiquitous in science, from the modeling of particles in Physics to prey-predator in Biology, to opinion dynamics in economics and social sciences, where the interaction law between agents yields a rich variety of collective dynamics. Inferring the interaction laws between agents from observational trajectory data is a fundamental task for modeling and prediction, yet challenging due to the implicit nonlinear forward map of the system and high dimensionality of the state space. Consequently, the algorithms often offer no guarantees and the resulting discoveries of interaction laws need external human validation.

Given abundant data sampled from multiple trajectories, we use tools from statistical/machine learning to construct estimators for interaction kernels with provably good statistical and computational properties, under the minimal assumptions that the interaction kernels only depend on pairwise distance. Numerical simulations on a variety of examples suggest the learnability of kernels in models used in practice, and that our estimators are robust to noise, and produced accurate predictions of collective dynamics in relative large time intervals, even when they are learned from data collected in short time intervals.

ALGEBRA SEMINAR
TITLE: Incidence Algebras
SPEAKER: Dony Varghese, UTK
TIME: 3:35 PM
ROOM: Ayres 114

Thursday, Nov. 5

ORAL SPECIALTY EXAM
SPEAKER: Shuler Hopkins, UTK
TIME: 9:00 am
ROOM: Ayres 114
His committee consists of Professors: Nicoara (Chair), Lind, and Richter.

GEOMETRIC ANALYSIS SEMINAR
Title: Stability of graphical tori with almost nonnegative scalar curvature
Speaker: Raquel Perales, National University of Mexico
Time: 4:00pm – 6:00pm
Room: Ayres 111
Abstract: By works of Schoen--Yau and Gromov--Lawson any Riemannian manifold with nonnegative scalar curvature and diffeomorphic to a torus is isometric to a flat torus. Gromov conjectured subconvergence of tori with respect to a weak Sobolev type metric when the scalar curvature goes to zero. We prove flat and intrinsic flat subconvergence to a flat torus for sequences of $3$-dimensional tori $M_j$ that can be realized as graphs of functions defined over flat tori satisfying a uniform upper diameter bound, a uniform lower bound on the area of the smallest closed minimal surface, and scalar curvature bounds of the form $R_{g_{M_j}} \geq -1/j$. We also show that the volume of the manifolds of the convergent subsequence converges to the volume of the limit space.  We do so adapting results of Huang-Lee and Huang-Lee-Sormani.

Friday, Nov. 6

ORAL SPECIALTY EXAM
SPEAKER: Tamara Riggs, UTK
TIME: 1:00 pm
ROOM: Ayres 114
Her committee consists of Professors: Nicoara (Chair), Lind, and Vellis.

COLLOQUIUM
TITLE: Applied differential geometry and harmonic analysis in deep learning regularization
SPEAKER: Wei Zhu, Duke University
TIME: 3:35 PM
ROOM: Ayres 405
Abstract: With the explosive production of digital data and information, data-driven methods, deep neural networks (DNNs) in particular, have revolutionized machine learning and scientific computing by gradually outperforming traditional hand-craft model-based algorithms. While DNNs have proved very successful when large training sets are available, they typically have two shortcomings: First, when the training data are scarce, DNNs tend to suffer from overfitting. Second, the generalization ability of overparameterized DNNs still remains a mystery despite many recent efforts.

In this talk, I will discuss two recent works to “inject” the “modeling” flavor back into deep learning to improve the generalization performance and interpretability of DNNs. This is accomplished by deep learning regularization through applied differential geometry and harmonic analysis. In the first part of the talk, I will explain how to improve the regularity of the DNN representation by imposing a “smoothness” inductive bias over the DNN model. This is achieved by solving a variational problem with a low-dimensionality constraint on the data-feature concatenation manifold. In the second part, I will discuss how to impose scale-equivariance in network representation by conducting joint convolutions across the space and the scaling group. The stability of the equivariant representation to nuisance input deformation is also proved under mild assumptions on the Fourier-Bessel norm of filter expansion coefficients.

#### If you are interested in giving or arranging a talk for one of our seminars or colloquiums, please review our calendar.

If you have questions, or a date you would like to confirm, please contact Dr. Christopher Strickland, cstric12@utk.edu

Past notices:

Nov. 25, 2019

Nov. 18, 2019

Nov. 11, 2019

Nov. 4, 2019

Oct. 28, 2019

Oct. 21, 2019

Oct. 14, 2019

Oct. 7, 2019

Sept. 30, 2019

Sept. 23, 2019

Sept. 16, 2019

Sept. 9, 2019

Sept. 2, 2019

Aug. 26, 2019

2018-19

2017-18

###### last updated: December 2019

Department of Mathematics
College of Arts & Sciences

227 Ayres Hall. 1403 Circle Drive. Knoxville TN 37996-1320
Phone: 865-974-2461 Fax: 865-974-6576 Email: math_info@utk.edu