Colloquia & Seminars

Abstract: Resistance to drugs is one of the most challenging problems in public health. In this talk, I will focus on drug resistance in cancer, which is often associated with the existence of resistant mutants in the evolving population of malignant cells. I will start by showing the type of stochastic modeling that has been used to quantify various aspects of resistance generation, including multiple-drug resistance, the role of cellular turnover, cellular quiescence, and the phenomenon of cross-resistance. I will compare and contrast treatment strategies such as cycling and simultaneous multi-drug treatment. I will then focus on a specific case of Chronic Lymphocytic Leukemia (CLL). This is the most common leukemia, mostly arising in patients over the age of 50. The disease has been treated with chemo-immunotherapies with varying outcomes, depending on the genetic make-up of the tumor cells. More recently, a promising tyrosine kinase inhibitor, ibrutinib, has been developed, which resulted in successful responses in clinical trials, even for the most aggressive chronic lymphocytic leukemia types. The crucial questions include how long disease control can be maintained in individual patients, when drug resistance is expected to arise, and what can be done to counter it. Computational evolutionary models, based on measured kinetic parameters of patients, allow us to address these questions and to pave the way toward a personalized prognosis and treatment.

Short Bio: Natalia Komarova holds an MS in Theoretical Physics from Moscow State University and a PhD in Applied Mathematics from University of Arizona. After being a Member at the Institute for Advanced Studies in Princeton (1999-2003), she became Assistant Professor at the Department of Mathematics at Rutgers, and then worked at UC Irvine from 2004 until 2024, when she joined UCSD. Komarova is interested in Applied Mathematics, and in particular, in Mathematical Biology, evolution, and modeling of complex social phenomena.

Abstract: Quantum computers are physical machines that process information using the principles of quantum mechanics, which in turn is underpinned by linear algebra. The talk will start with a review of Lie algebras (consisting of matrices under the operation of commutator) and their role in quantum mechanics. The dynamical Lie algebra (DLA) of a quantum system is defined as the Lie algebra obtained by taking all real linear combinations and nested commutators of the terms of the Hamiltonian. The significance of the DLA is that the time evolution of the system is given by elements of the associated Lie group. The DLA determines the set of reachable states of the system and its controllability, so it is relevant for designing quantum circuits. In this talk, I will present a classification of DLAs generated by 2-local Pauli interactions on spin chains and on arbitrary interaction graphs. I will also discuss applications of DLAs to variational quantum computing, including the problem of barren plateaus. The talk will be accessible to all mathematics graduate students; no prior knowledge of physics or quantum computing is assumed.

Short Bio: Originally from Bulgaria, Bojko Bakalov received his PhD from MIT and was a Miller Research Fellow at UC Berkeley before joining the NC State Math Department in 2003. Currently, he is the Director of Graduate Programs in Math and Applied Math, and has a leadership role in the NC State Quantum Initiative. Bakalov’s research interests include representation theory, quantum computing, mathematical physics, signal processing, and integrable systems. In 2006, he was awarded the Hermann Weyl Prize of the International Colloquia on Group Theoretical Methods in Physics, for original work of significant scientific quality in the area of understanding physics through symmetries. Bakalov’s research has been funded by the US Air Force, DOE, NSA, NSF, and the Simons Foundation.

Abstract: In the normal heart, intracardiac blood flow (hemodynamics) optimizes pumping efficiency by facilitating the motion of blood in and out of the heart and closure of valves. Abnormal blood flow patterns that occur due to heart disease can be detrimental: both due to decreasing cardiac efficiency, and to the sensitivity of heart cells to abnormal hemodynamic stresses, which could exacerbate pathological progression of heart disease. In this talk, we will focus on hypertrophic cardiomyopathy (HCM), a congenital heart disease characterized by thickening of the left ventricular wall (hypertrophy) that leads to altered cardiac flow patterns. We will discuss how computational modeling approaches can be used in the evaluation of HCM patients and the effect of novel myosin inhibitor drugs to treat HCM. This work is in collaboration with Dr. Ted Abraham (UCSF HCM Center of Excellence).

Short Bio: Sandra Rugonyi, Professor of Biomedical Engineering, Oregon Health & Science University (OHSU), Portland, OR, USA. Prof. Rugonyi has expertise in cardiovascular biomechanics and computational modelling. Her career started in Argentina, where she got an MS-equivalent degree in Nuclear Engineering from the Balseiro Institute. After working for a nuclear power plant and then a steel company, she moved to the USA, where she earned a PhD in Mechanical Engineering from MIT that focused on advanced numerical methods for fluid-structure interaction problems. In 2005 Dr. Rugonyi joined the Biomedical Engineering department at OHSU, and since then she has applied mechanical engineering principles to heart development and congenital heart disease. Dr. Rugonyi has contributed to fundamental understanding of hemodynamic regulation on heart formation.

Abstract: In this talk, we will provide an overview of the ill-posed inverse problem in Diffuse Optical Tomography (DOT) at an introductory level. We will discuss several regularization approaches to solve the ill-posed inverse problem in DOT including deterministic, statistical, and machine learning. Then we will present our most recent work using Bayesian Inversion Using level sets for image reconstruction in DOT. The results of image reconstruction will be demonstrated using synthetic data for the recently proposed algorithm. This is joint work with Anuj Abhishek (Case Western Reserve University) and Thilo Strauss (Xi’an Jiaotong-Liverpool University).

Short Bio: Taufiquar Khan is currently a Professor and the Chair of the Department of Mathematics and Statistics, University of North Carolina at Charlotte (UNC Charlotte). He was a Professor and an Associate Director of Graduate Studies of the School of Mathematical and Statistical Sciences, Clemson University, Clemson, SC, USA, before joining UNC Charlotte. He is a recipient of the Humboldt Fellowship from Germany. His research interests include machine learning, inverse problems involving ordinary and partial differential equations. His present and past research have been supported through the NSF, DOD, Humboldt Foundation, and the industry.

Abstract: In recent years, we have seen a large body of research using hierarchical matrix algebra to construct low complexity linear solvers and preconditioners. Not only can these fast solvers significantly accelerate the speed of large-scale PDE-based simulations, but also they can speed up many AI and machine learning algorithms, which are often matrix-computation-bound. On the other hand, statistical and machine learning methods can be used to help select the best solvers or solvers' configurations for specific problems and computer platforms. In both of these fields, high-performance computing becomes an indispensable cross-cutting tool for achieving real-time solutions for big data problems. In this talk, we will show our recent developments in the intersection of these areas.

Short Bio: Dr. Xiaoye S. Li is a Senior Scientist in the Computational Research Division, Lawrence Berkeley National Laboratory. Dr. Li earned her Ph.D. in Computer Science from UC Berkeley in 1996, MS in Math & Computer Science from Penn State Univ., and B.S. in Computer Science from Tsinghua Univ. She has worked on diverse problems in high-performance scientific computations, including parallel computing and sparse matrix computations. She has authored over 130 publications, and is the lead developer of SuperLU, a widely-used sparse direct solver, and has contributed to the development of several other mathematical libraries, including LAPACK and XBLAS. She has served on the editorial boards of ACM Trans. Math. Software, IJHPCA, and SIAM J. Scientific Comput., as well as many program committees of scientific conferences. She is a Fellow of SIAM and a Senior Member of ACM.

Abstract: The immune system is able to fight cancer by mustering and training an army of effector “killer” cells. Mathematical models of tumor-immune interactions must describe the proliferation, recruiting, and killing rates of immune cells. Earlier work surprisingly showed that the functions describing the kill rates distinguish between two types of immune cells. The mechanisms behind these differences have been a mystery, however. In an attempt to unravel this mystery, we have created a cell-based fixed-lattice model that simulates immune cell and tumor cell interaction involving MHC recognition, and two killing mechanisms. These mechanisms play a big role in the effectiveness of many cancer immunotherapies. Results from model simulations, along with theories developed by ecologists, can help to illuminate which mechanisms are at work in different conditions.