ALT The UCI Math Department hosts a special seminar called "Toward Equitable Outcomes for Math Majors" by the SELC Project, located in ISEB 1310 on May 10, 2024 at 3-4 pm.

ALT The UCI Math Department hosts a colloquium on "Fractalization, Quantization, and Revivals in Dispersive Systems" by Peter J. Olver from University of Minnesota, Twin Cities. It will be held at Rowland Hall 306 at 4-5 PM on February 8, 2024. Abstract: Dispersive quantization, also known as the Talbot effect describes the remarkable evolution, through spatially periodic linear dispersion, of rough initial data, producing fractal, non-differentiable profiles at irrational times and, for asymptotically polynomial dispersion relations, quantized structures and revivals at rational times. Such phenomena have been observed in dispersive waves, optics, and quantum mechanics, and have intriguing connections with number theoretic exponential sums. I will present recent results on the analysis and numerics for linear and nonlinear dispersive wave models, both integrable and non-integrable, as well as integro-differential equations modeling interface dynamics and Fermi-Pasta-Ulam-Tsingou

ALT The UCI Math Department hosts a seminar on "A Theory of Neuronal Synaptic Balance" by Pierre Baldi, invited by Roman Vershynin. It will be held at Rowland Hall 510R at 2-3 PM on February 7, 2024.

ALT The UCI Math Department hosts a seminar on "Presentations of Derived Categories" by Reginald Anderson from Claremont McKenna College, invited by Jesse Wolfson. It will be held at Rowland Hall 510R at 1-2 PM on February 1, 2024. Abstract: The bounded derived category of coherent sheaves gives an isomorphism invariant for smooth projective varieties which are Fano or general type. King conjectured in 1997 that any smooth complete toric variety has a strong, full exceptional collection of line bundles. King's conjecture was proven false, but determining the exact criteria for a smooth complete (weak-)Fano toric variety to have a strong full exceptional collection of line bundles remains open, as does finding a method to generate this SFEC of line bundles for varieties which admit such a collection. In this talk I will give a cellular resolution of the diagonal for smooth projective toric varieties which yields a SFEC of line bundles on unimodular toric surfaces, as well as for a

ALT The UCI Math Department hosts a seminar on "Homological Percolation on a Torus" by Paul Duncan from Israel's Hebrew University of Jerusalem. It will be held at Rowland Hall 510R at 2-3 PM. Abstract: Many well-studied properties of random graphs have interesting generalizations to higher dimensions in random simplicial complexes. We will discuss a version of percolation in which, instead of edges, we add two (or higher)-dimensional cubes to a subcomplex of a large torus at random. In this setting, we see a phase transition that marks the appearance of giant "sheets," analogous to the appearance of giant components in graph models. This phenomenon is most naturally described in the language of algebraic topology, but this talk will not assume any topological background. Based on joint work with Ben Schweinhart and Matt Kahle.

ALT The UCI Math Department hosts a seminar on "Non-Stationary Anderson Localization" by Victor Kleptsyn from France's University of Rennes I. It will be held at Rowland Hall 440R at 2-3 PM. Abstract: Using recent results on dynamics of non-stationary random matrix products, we establish spectral and dynamical localization for 1D Schrodinger operators with potentials given by independent but not identically distributed random variables.

ALT The UCI Math Department hosts a colloquium on "Anti-Classification Results in Smooth Ergodic Theory" by Marlies Gerber of Indiana University. She was invited by Matthew Foreman and her work builds off of what Foreman and his colleagues have done. Abstract: We consider the complexity of the problem of classifying ergodic automorphisms up to isomorphism or up to Kakutani equivalence. For example, are these equivalence relations, considered as subsets of the Cartesian product of the space of ergodic automorphisms with itself, Borel sets? The first breakthroughs were the anti-classification results of Foreman, Rudolph, and Weiss for isomorphism of ergodic automorphisms, and the subsequent anti-classification results of Foreman and Weiss for isomorphism of ergodic automorphisms that are also smooth diffeomorphisms preserving a given smooth measure on a manifold.

ALT The UCI Math Department hosts a seminar on "A Degree One Carleson Operator Along the Paraboloid" by Lars Becker of the University of Bonn. He is a second year PhD student under the supervision of Christoph Thiele. My research interests are in harmonic analysis, more specifically I am interested in generalizations of Carleson's theorem, and in finding the optimal constants in classical Fourier extension inequalities.

ALT If you wanna show how well you can share your work in three fewer minutes, apply to the Grad Slam! The deadline for the Grad Slam is this Sunday, January 21. Apply now!

ALT UCI Math Department Special Colloquium: Why Can Kontsevich's Invariants Detect Exotic Phenomena? Presented by Junior Fellow Xujia Chen of the Harvard Society of Fellows at Room 1201 of Natural Sciences II on January 19, 2024. How to understand the role smooth structure plays in Kontsevich's invariants? The difference between the category of smooth manifolds and the category of topological manifolds has always been a delicate and intriguing problem, called the "exotic phenomena". Kontsevich's invariants, defined by Kontsevich in the early 1990s from perturbative Chern-Simons theory, are invariants of (certain) 3-manifolds / fiber bundles / knots and links (it is the same argument in different settings). The recent work of Watanabe (2018) uses Kontsevich's invariants to show that the group of diffeomorphisms of the 4-dimensional ball, as a topological group, has non-trivial homotopy type. In contrast, the group of homeomorphisms of the 4-dimensional ball is contractible. This implies tha