Plenary Speakers

Talk Title: The small data global well-posedness conjecture for defocusing dispersive flows
Abstract: The long-time dynamics of solutions in nonlinear dispersive flows are determined by competing effects of dispersion on one hand and nonlinear wave interactions on the other hand.   This talk  will present a very recent conjecture which broadly asserts that small data should yield global solutions for  1D defocusing dispersive flows with cubic nonlinearities, in both semilinear and quasilinear settings. We will also discuss some higher dimensional extensions of this conjecture. This is joint work with Daniel Tataru.

Bio: Mihaela Ifrim received her Ph.D. in Mathematics from the University of California, Davis, and is currently a Professor of Mathematics at the University of Wisconsin–Madison. Her research focuses on nonlinear wave and dispersive equations, fluid mechanics, and harmonic analysis. Professor Ifrim has developed new analytical frameworks for global well-posedness, long-time dynamics, and scattering in both semilinear and quasilinear dispersive flows, including nonlinear Schrödinger equations, Dirac models, and free-boundary problems such as water waves. She is the recipient of numerous honors, including a Sloan Research Fellowship, an NSF CAREER Award, and the Presidential Early Career Award for Scientists and Engineers (PECASE), the highest honor bestowed by the U.S. government on early-career scientists and engineers. 

Talk Title: Mathematical AI and Applications
Abstract: Despite the tremendous success of artificial intelligence (AI) in science, engineering, and technology in the past decade, its explainability and generalizability have been a major concern. Additionally, AI-based discovery encounters challenges arising from intricate complexity, high dimensionality, nonlinearity, and multiscale nature in many data. The solution to these challenges holds the future of AI. Topological deep learning (TDL), a new frontier in rational learning introduced by us in 2017, offers interpretable and generalized AI approaches. TDL utilizes topological data analysis (TDA), which is originally rooted in persistent homology, an algebraic topology technique for point cloud data. Recently, much effort has been given to the generalization of TDA to combinatoric spectral theory, differential topology, and geometric topology to tackle data on graphs, differentiable manifolds, and curves embedded in 3-space, respectively (see arXiv:2507.19504 for a review). Moreover, commutative algebra has emerged as a new paradigm in Math AI. These approaches reduce dimensionality, simplify geometric complexity, capture high-order interactions, and provide interpretable AI models in a manner that cannot be achieved through other mathematical, statistical, and physical methodologies. I will discuss compelling applications which consistently demonstrate the advantages of Math AI over competing methods. 

Bio: Guowei Wei received his Ph.D. degree from the University of British Columbia and is currently an MSU Research Foundation Professor at Michigan State University. His research focuses on the mathematical foundations of biosciences and artificial intelligence (AI).  Dr. Wei and his coworkers pioneered many mathematical AI paradigms, such as topological deep learning (TDL), manifold topological learning (MTL), and commutative algebra learning (CAL) that integrate profound mathematical structures with AI to tackle data challenges. Their mathematical AI has led to victories in D3R Grand Challenges, a worldwide annual competition series in computer-aided drug design. Using TDL, genotyping, and computational biophysics, the Wei team unveiled the mechanisms of SARS-CoV-2 evolution and successfully predicted emerging dominant SARS-CoV-2 variants.     

Talk Title: The dynamics of organelle positioning and scaling inside of living cells
Abstract: Within cells, centrosomes are mobile nucleating sites for arrays of growing and disassembling microtubules. The centrosomal array is an adaptable and fundamental force-bearing and force-producing structure used by cells to, for example, move nuclei and spindles into their proper places as the cell moves towards cell division. I'll discuss mathematical models of coarse-grained centrosomal arrays and and their interaction with molecular motors and the cellular geometry. This takes the form of ODEs for centrosome position driven by an integral coupling to surface density fields of motor-binding probability. I'll talk about the model's interesting mathematical structure and what dynamics it predicts for simple cellular geometries. I'll then show that in more complex settings the model can quantitatively predict how cellular nuclei, through their mechanical coupling to centrosomal arrays, migrate and move together into so-called "proper position" to form a spindle before cell division, and how the model predicts the scaling of spindle length across large changes in cell size.   

Bio: Dr. Michael J. Shelley is an applied mathematician who works on the modeling and simulation of complex systems arising in physics and biology. He is the Lyttle Professor of Applied Mathematics at the Courant Institute, co-founder of the Courant Institute's Applied Mathematics Lab, and is the Director of the Center for Computational Biology at the Flatiron Institute.  He holds a B.A. in mathematics from the University of Colorado and a Ph.D. in applied mathematics from the University of Arizona. He was a postdoctoral researcher at Princeton University and a member of the mathematics faculty at the University of Chicago before joining NYU. Shelley has received the François Frenkiel Award from the American Physical Society and the Julian Cole Lectureship from the Society for Industrial and Applied Mathematics, and he is a Fellow of both societies. He is also a Fellow of the American Academy of Arts and Sciences and a member of the National Academy of Sciences.