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Colloquia and Seminars

The Department of Mathematics is home to a dynamic group of scholars who regularly share their expertise with others. Many of our events and activities are free and open to the public, and we encourage you to get involved.


Colloquia 2019

JAN 15 - Leonardo Zepeda-Nunez - Accelerating Ab-Initio Molecular Dynamics Via Multi-Scale Neural Networks

When: Tuesday, January 15, 2019  - 4:30 p.m. to 5:30 p.m.
Where: LeConte 412 (map)

Speaker: Leonardo Zepeda-Nunez, Lawrence Berkeley National Laboratory

Abstract: Deep learning has rapidly become a large field with an ever-growing range of applications; however, its intersection with scientific computing remains in its infancy, mainly due to the high accuracy that scientific computing problems require, which depends greatly on the architecture of the neural network.

In this talk we present a novel deep neural network with a multi-scale architecture inspired in H-matrices (and H2-matrices) to efficiently approximate, within 3-4 digits, several challenging non-linear maps arising from the discretization of PDEs, whose evaluation would otherwise require computationally intensive iterative methods.

In particular, we focus on the notoriously difficult Kohn-Sham map arising from Density Functional Theory (DFT). We show that the proposed multiscale-neural network can efficiently learn this map, thus bypassing an expensive self-consistent field iteration. In addition, we show the application of this methodology to ab-initio molecular dynamics, for which we provide examples for 1D problems and small, albeit realistic, 3D systems.

Joint work with Y. Fan, J. Feliu-Faaba, L. Lin, W. Jia, and L. Ying. [PDF]

JAN 24 - Maziar Raissi - Hidden Physics Models: Machine Learning of Non-Linear Partial Differential Equations
When: Thursday, January 24, 2019  - 4:30 p.m. to 5:30 p.m.

Where: LeConte 412 (map)

Speaker: Maziar Raissi, Brown University

Abstract: grand challenge with great opportunities is to develop a coherent framework that enables blending conservation laws, physical principles, and/or phenomenological behaviours expressed by differential equations with the vast data sets available in many fields of engineering, science, and technology. At the intersection of probabilistic machine learning, deep learning, and scientific computations, this work is pursuing the overall vision to establish promising new directions for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data. To materialize this vision, this work is exploring two complementary directions: (1) designing data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and non-linear differential equations, to extract patterns from high-dimensional data generated from experiments, and (2) designing novel numerical algorithms that can seamlessly blend equations and noisy multi-fidelity data, infer latent quantities of interest (e.g., the solution to a differential equation), and naturally quantify uncertainty in computations. The latter is aligned in spirit with the emerging field of probabilistic numerics. [PDF]


Colloquia 2018

JAN 25 - Zhen-qing Chen - Anomalous Diffusions and Fractional Order Differential Equations

When: Thursday, January 25, 2018  - 4:30 p.m. to 5:30 p.m.
Where: LeConte 412 (map)

Speaker: Zhen-qing Chen, University of Washington

Abstract: Anomalous diffusion phenomenon has been observed in many natural systems, from the signalling of biological cells, to the foraging behaviour of animals, to the travel times of contaminants in groundwater. In this talk, I will first discuss the interplay between anomalous diffusions and differential equations of fractional order. I will then present some recent results in the study of these two topics, including the counterpart of DeGiorgi-Nash-Moser-Aronson theory for non-local operators of fractional order. No prior knowledge in these two subjects is assumed. [PDF]

Host: Hong Wang

FEB 8 - Changhui Tan - Self-organized dynamics: Aggregation and Flocking

When: Thursday, February 8, 2018 - 4:30 p.m. to 5:30 p.m.
Where: LeConte 412 (map)

Speaker: Changhui Tan, Rice University

Abstract: Self-organized behaviors are commonly observed in nature and human societies, such as bird flocks, fish swarms and human crowds. In this talk, I will present some celebrated mathematical models, with simple small-scale interactions that lead to the emergence of global behaviors: aggregation and flocking. The models can be constructed through a multiscale framework: from microscopic agent-based dynamics, to macroscopic fluid systems. I will discuss some recent analytical and numerical results on the derivation of the systems in different scales, global wellposedness theory, large time behaviors, as well as interesting connections to some classical equations in fluid mechanics. [PDF]

FEB 15 - Andrei Tarfulea - Bounds and Aymptotic Dynamics for Nonlinear Evolution Equations

When: Thursday, February 15, 2018 - 4:30 p.m. to 5:30 p.m.
Where: LeConte 412 (map)

Speaker: Andrei Tarfulea, University of Chicago

Abstract: Understanding the behavior of solutions to physically motivated evolution equations is one of the most important areas of applied analysis. Developing strong bounds and asymptotics are crucial for anticipating the behavior of simulations, simplifying the methods needed to model the physical phenomena. The focus will be on recent results in three physical models: homogenization and asymptotics for nonlocal reaction-diffusion equations, a priori bounds for hydrodynamic equations with thermal effects, and the local well-posedness for the Landau equation (with initial data that is large, away from Maxwellian, and containing vacuum regions). Each problem presents unique challenges arising from the nonlinearity and/or nonlocality of the equation, and the emphasis will be on the different methods and techniques used to treat those difficulties in each case. The talk will touch on novelties in viscosity theory and precision in nonlocal front propagation for reaction-diffusion equations, as well as the emergence of "dynamic" self-regularization in the thermal hydrodynamic and Landau equations. [PDF]

FEB 20 - Xiu Yang - Uncertainty Quantification for Complex Systems using Limited Data

When: Tuesday, February 20, 2018 - 4:30 p.m. to 5:30 p.m.
Where: LeConte 412 (map)

Speaker: Xiu Yang, PNNL

Abstract: Realistic analysis and design of complex engineering systems require not only a fine understanding of the underlying physics, but also a significant recognition of uncertainties and their influences on the quantities of interest. Intrinsic variabilities and lack of knowledge about system parameters or governing physical models often considerably affect quantities of interest and decision-making processes. For complex systems, the available data for quantifying uncertainties or analyzing sensitivities are usually limited because the cost of conducting a large number of experiments or running many large-scale simulations can be prohibitive. Efficient approaches of representing uncertainties using limited data are critical for such problems. I will talk about two approaches for uncertainty quantification by constructing surrogate model of the quantity of interest. The first method is the adaptive functional ANOVA method, which constructs the surrogate model hierarchically by analyzing the sensitivities of individual parameters. The second method is the sparse regression based on identification of low-dimensional structure, which exploits low-dimensional structures in the parameter space and solves an optimization problem to construct the surrogate models. I will demonstrate the efficiency of these methods with PDE with random parameters as well as applications in aerodynamics and computational chemistry. [PDF]

FEB 22 - Daniel Krashen - Topological Viewpoints on Algebraic Complexity

When: Thursday, February 22, 2018 - 4:30 p.m. to 5:30 p.m.
Where: LeConte 412 (map)

Speaker: Daniel Krashen, Rutgers University/University of Georgia

 Abstract: Understanding algebraic structures such as Galois extensions, quadratic forms and division algebras, can give important insights into the arithmetic of fields. In this talk, I will discuss recent work showing ways in which the arithmetic of certain fields can be partially described by topological information. I will then describe how these observations lead to arithmetic versions of the Meyer-Vietoris sequences, the Seifert–van Kampen theorem, and examples and counterexamples to local-global principles. [PDF]

Host: Frank Thorne

MAR 1 - Lars Christensen - Quotients of the Polynomial Algebra in Three Variables

When: Thursday, March 1, 2018 - 4:30 p.m. to 5:30 p.m.
Where: LeConte 412 (map)

Speaker: Lars Christensen, Texas Tech University

Abstract: Let K be a field, for example that of complex numbers, and let R be a quotient of the polynomial algebra \(Q = K [x,y,z]\). The minimal free resolution of R as a module over Q is a sequence of linear maps between free Q-modules. One may think of such free resolutions as the result of a linearization process that unwinds the structure of R in a
series of maps. This point of view, which goes back to Hilbert, already yields a wealth of information about R, but there is more to the picture: The resolution carries a multiplicative structure; it is itself a ring! For algebraists this is  Gefundenes Fressen, and in the talk I will discuss what kind of questions this structure has helped answer and what new questions it raises. [PDF]

Host: Andrew Kustin

APR 5 - Anthony Bonato - Graph Searching Games and Probabilistic Methods

When:  Thursday, April 5, 2018  - 4:30 p.m. to 5:30 p.m.
Where: LeConte 412 (map)

Speaker: Anthony Bonato, Ryerson University

Abstract: The intersection of graph searching and probabilistic methods is a new topic within graph theory, with applications to graph searching problems such as the game of Cops and Robbers and its many variants, Firefighting, graph burning, and acquaintance time. Graph searching games may be played on random structures such as binomial random graphs, random regular graphs or random geometric graphs. Probabilistic methods may also be used to understand the properties of games played on deterministic structures. A third and new approach is where randomness figures into the rules of the game, such as in the game of Zombies and Survivors. We give a broad survey of graph searching and probabilistic methods, highlighting the themes and trends in this emerging area. The talk is based on my book (with the same title) co-authored with Pawel Pralat published by CRC Press. [PDF]

Bio: Anthony Bonato’s research is in Graph Theory, with applications to the modelling of real-world, complex networks such as the web graph and on-line social networks. He has authored over 110 papers and three books with 70 co-authors. He has delivered over 30 invited addresses at international conferences in North America, Europe, China, and India. He twice won the Ryerson Faculty Research Award for excellence in research and an inaugural Outstanding Contribution to Graduate Education Award. He is the Chair of the Pure Mathematics Section of the NSERC Discovery Mathematics and Statistics Evaluation Group, Editor-in-Chief of the journal Internet Mathematics, and editor of the journal Contributions to Discrete Mathematics.

Host: Linyuan Lu

APR 27 - Richard Anstee - Forbidden Configurations

When:  Friday, April 27, 2018  - 3:30 p.m. to 4:30 p.m.
Where: LeConte 412 (map)

Speaker: Richard Anstee, The University of British Columbia

This is a special Colloquium and reception in honor of Jerry Griggs' retirement

Abstract: Extremal Combinatorics asks how many sets (or other objects) can you have while satisfying some property (often the property of avoiding some structure). We encode a family of n subsets of elements {1,2,..,m} using an element-subset (0,1)-incidence matrix. A matrix is simple if it has no repeated columns. Given a pxq (0,1)-matrix F, we say a (0,1)-matrix A has F as a confi guration if there is submatrix of A which is a row and column permutation of F. We then defi ne our extremal function forb(m,F) as the maximum number of columns of any m-rowed simple (0,1)-matrix which does have F as a confi guration. Jerry was involved in some of the initial work on this problem and the construction that led to an attractive conjecture. Two recent results are discussed. One (with Salazar) concerns extending a pxq confi guration F to a family of all possible pxq confi gurations G with F less than or equal to G (i.e. only the 1's matter). The conjecture does not extend to this setting but there are interesting connections to other extremal problems. The second (with Dawson, Lu and Sali) considers extending the extremal problem to (0,1,2)-matrices. We consider a family of (0,1,2)-matrices which appears to have behaviour analogous to (0,1)-matrices. Ramsey type theorems are used and obtained. [PDF]

Host:  Linyuan Lu

NOV 8 - Paul S. Aspinwall - Why String Theory Prefers Algebraic Geometry

When: Thursday, November 8, 2018  - 4:30 p.m. to 5:30 p.m.
Where: LeConte 412 (map)

Speaker: Paul S. Aspinwall, Duke University

Abstract: Superstring theory is hoped to provide a theory of all fundamental physics including an understanding of quantum gravity. While theoretical physicists like to describe spacetime in terms of differential geometry, we will show how stringy geometry is better explained in terms of representation theory of certain algebras and this can be more easily described in terms of algebraic geometry. We will discuss how mirror symmetry arises and how the derived category of coherent sheaves is useful in this context. [PDF]

Host:  Matthew Ballard

NOV 15 - Claudio Canuto - Subsurface Flow Simulations in Stochastic Discrete Fracture Networks

When: Thursday, November 15, 2018  - 4:30 p.m. to 5:30 p.m.
Where: LeConte 412 (map)

Speaker: Claudio Canuto, Politecnico di Torino

Abstract: Discrete Fracture Network (DFN) models are widely used in the simulation of subsurface flows; they describe a geological reservoir as a system of many intersecting planar polygons representing the underground network of fractures. The mathematical description is based on Darcy’s law, supplemented by appropriate interface conditions at each intersection between two fractures. Efficient numerical discretizations, based on the reformulation of the equations as a pde-constrained optimization problem, allow for a totally independent meshing of each fracture.
We consider stochastic versions of DFN, in which certain relevant parameters of the models are assumed to be random variables with given probability distribution. The dependence of the quantity of interest upon these variables may be smooth (e.g., analytic) or non-smooth (e.g., discontinuous). We perform a non-intrusive uncertainty quantification analysis which, according to the different situations, uses such tools as stochastic collocation, multilevel MonteCarlo, or multifidelity strategies. [PDF]

Host:  Wolfgang Dahmen

DEC 7 - Bruce C. Berndt - Living with Ramanujan for Forty Years

When: Friday, December 7, 2018  - 4:30 p.m. to 5:30 p.m.
Where: LeConte 412 (map)

Speaker: Bruce C. Berndt, University of Illinois at Champaign-Urbana

Abstract: Beginning in May, 1977, the speaker began to devote all of his research efforts to proving the approximately 3300 claims made by Ramanujan without proofs in his notebooks. While completing this task a little over 20 years later, with the help, principally, of his graduate students, he began to work with George Andrews on proving Ramanujan's claims from his "lost notebook.” After another 20 years, with the help of several mathematicians, including my doctoral students, Andrews and I think all the claims in the lost notebook have now been proved. One entry from the lost notebook connected with the famous Dirichlet Divisor Problem remained painfully difficult to prove. Borrowing from Sherlock Holmes, G.N. Watson's retiring address to the London Mathematical Society in November, 1935 was on the "final problem," arising from Ramanujan's last letter to Hardy. Accordingly, we have called this entry the "final problem," because it was the last entry from the lost notebook to be proved. Early this summer, a proof was finally given by Junxian Li, who just completed her doctorate at the University of Illinois, Alexandru Zaharescu (her advisor), and myself. Since I will tell you how I became interested in Ramanujan and his notebooks, part of my lecture will be historical. [PDF]

Host:  Michael Filaseta