2019
Special Math Seminar in honor of Josephine Johansen: Faster, Safer, Healthier with Operations Research
Sommer Gentry, Professor of Mathematics, U.S. Naval Academy.
May 15, 2019
12-1:15 p.m.
Armitage 121
Talk will be followed by a catered lunch in West ABC in the campus center.
-
While mathematical advances of all sorts have impacted our world for the better, operations research is a branch of mathematics that is expressly focused on applying advanced analytical methods to help make better decisions. Operations researchers have eased traffic jams by closing selected streets, and gotten packages to you more quickly by planning U.P.S. routes with fewer left turns. Operations researchers have shown which personal decisions are the leading causes of death, and planned maintenance schedules to minimize bridge collapses. The mathematical tools of operations research, like using random numbers to simulate a range of outcomes when some data are unknown, or finding clever algorithms that shortcut the need to try every possible decision in order to find the best one, can be recycled to solve problems everywhere in our world. These days, I am using O.R. to increase the supply of kidneys available for patients who need a transplant, and to make organ allocation more equitable to patients across the U.S. In this talk, I will describe some of my O.R. forays into far-flung fields, and tell my favorite stories about O.R.
Math Seminar: Classical and Machine-Learning Methods for Quantum Simulation
Thomas F. Miller III, Professor of Chemistry, Division of Chemistry and Chemical Engineering, California Institute of Technology (CALTECH)
April 12, 2019
11:20-12:20
Business and Science Building (BSB), Room 334
-
A focus of my research is to the develop simulation methods that reveal the mechanistic details of quantum mechanical reactions that are central to biological, molecular, and heterogenous catalysis. The nature of this effort is three-fold: we combine quantum statistical mechanics and semiclassical dynamics methods to expand the scope and reliability of condensed-phase quantum dynamics simulation; we develop quantum embedding and machine learning methods that improve the description of molecular interactions and electronic properties; and we apply these methods to understand complex chemical systems. The talk will focus on recent developments [1] and applications [2] of Feynman path integral methods for the description of non-adiabatic chemical dynamics, including proton-coupled electron-transfer and long-ranged electron transfer in protein systems. Additionally, we will describe a machine-learning approach [3,4] to predicting the electronic structure results on the basis of simple molecular orbitals properties, yielding striking accuracy and transferability across chemical systems at low computational cost.
[1] “Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics.” X. Tao, P. Shushkov, and T. F. Miller III, J. Chem. Phys., 148, 102327 (2018).
[2] “Fluctuating hydrogen-bond networks govern anomalous electron transfer kinetics in a blue copper protein.” J. S. Kretchmer, N. Boekelheide, J. J. Warren, J. R. Winkler, H. B. Gray, and T. F. Miller III, Proc. Natl. Acad. Sci. USA, 115, 6129 (2018).
[3] “Transferability in machine learning for electronic structure via the molecular orbital basis.” M. Welborn, L. Cheng, and T. F. Miller III, J. Chem. Theory Comput., 14, 4772 (2018).
[4] “A universal density matrix functional from molecular orbital-based machine learning: Transferability across organic molecules.” L. Cheng, M. Welborn, and T. F. Miller III, arXiv:1901.03309 (2019).
Math Seminar: Non-local Navier-Stokes equations
Camillo De Lellis, Institute of Advanced Study in Princeton, NJ
February 22, 2019
11:20-12:20
Armitage Hall Room 121
-
I will consider a variant of the Navier-Stokes equations, where the classical Laplacian is substituted by a fractional Laplacian $-(-\Delta)^\alpha$. I will present two results. In the hypodissipative case, i.e. when $\alpha$ is sufficiently small, in a joint work with Maria Colombo and Luigi De Rosa we show that Leray solutions are ill-posed. In the hyperdissipative case, i.e. when $\alpha>1$, in a joint work with Maria Colombo and Annalisa Massaccesi we prove a “strong analog” of the Caffarelli-Kohn-Nirenberg Theorem, which strengthens the conclusions of a previous work by Katz and Pavlovic.
Math Seminar: Mixing and the Glass Transition
Aaron Smith, University of Ottawa, Department of Mathematics and Statistics
February 1, 2019
11:20-12:20
Business and Science Building BSB 334
-
Supercooled liquid forms when a liquid is cooled below its usual freezing temperature without entering a crystalline solid phase. As supercooled liquids continue to get colder, they exhibit something called the glass transition: they remain disordered, but start to otherwise behave much like solids. This glass transition is important for many materials, including rubbers and colloids, but is not theoretically well-understood. In this talk I will introduce a simple model for the glass transition that is easy to understand but difficult to study. I will then introduce two related families of models, introduced by physicists, that seem to give similar “glassy” behavior. Finally, I will present some heuristics and recent results on the relaxation and mixing behavior of these two models. My results in this talk are from joint and ongoing work with Paul Chleboun, Alessandra Faggionato, Fabio Martinelli, Natesh Pillai and Cristina Toninelli.