A convex continuous function can be determined, up to a constant, by its remoteness (distance of the subdifferential to zero). Based on this result, we discuss possible extensions in three directions: robustness (sensitivity analysis), slope determination (in the Lipschitz framework) and general determination theory. Zoom meeting: Link
Transition paths connecting metastable states are significant in science and engineering, such as in biochemical reactions. In this talk, I will present a stochastic optimal control formulation for transition path problems over an infinite time horizon, modeled by Markov jump processes on Polish spaces. An unbounded terminal cost at a stopping time and a running…
1. Kelsey Hanser Title : Greedy Kohnert Posets Abstract : K-Kohnert polynomials form a large family of polynomials which generalize Lascoux polynomials. Each K-Kohnert polynomial encodes a certain collection of diagrams which is formed from an initial seed diagram by applying what are called “Kohnert" and “ghost moves." In particular, Kohnert polynomials are the restrictions…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of invariants and designing methods and algorithms to compute them remains an active area of ongoing research with an abundance of applications, in particular, to…
Please save the date for the Department of Mathematics Spring 2024 Graduation Ceremony. Commencement starts at 5:30PM, with guest seating starting at 5:00PM.
Discover the beauty of mathematics and its wide applicability and power in everyday life! Grade Level: High School Students Schedule of Events: 11-11:15 am Drop Off 11:15-11:30 am Introductions 11:30-12:30 pm Applied Math and Math Modeling 12:30-1:15 pm Lunch 1:15-2:15 pm Control and Optimization in Biomedicine 2:15-2:45 pm Closing Remarks and Snacks 2:45-3 pm…
Cauchy's determinantal identity (1840s) expands via Schur polynomials the determinant of the matrix f, where f(t) = 1/(1-t) is applied entrywise to the rank-one matrix u v^T = (u_i v_j). This theme has resurfaced in the 2010s in analysis (following a 1960s computation by Loewner), in the quest to find polynomials p(t) with a negative coefficient that entrywise preserve…
Biology is defined by non-linear reactions caused by numerous molecular components interacting inside living cells. The complexity of such systems has limited classical experimental approaches in their capacity to measure living biological networks. This talk will explore how new computational tools derived from artificial intelligence are currently applied to study complex biological networks in living…
In this talk we will discuss the differences in the methodology of determining time-dependent and time-independent coefficients appearing in a hyperbolic equation in a Riemannian manifold. The talk is based on two recent research projects: 1) We will prove that a local source-to-solution map of a hyperbolic partial differential operator on a complete Riemannian manifold (no…
We will have Howling Cow ice cream at 3:45 in SAS 4104. The departmental meeting will start at 4:15pm in SAS 4201.
Developing robust and accurate data-based models for dynamical systems originating from plasma physics and hydrodynamics is of paramount importance. These applications pose several challenges, including the presence of multiple scales in time and space and a limited number of data, which is often noisy or inconsistent. The aim of structure-preserving ML is to strongly enforce…
I wanted to invite all of you to our Department of Mathematics Fall Picnic. We will be holding it at The Corner on Centennial Campus from 12-2 pm on August 24th. We look forward to seeing you and hope you will then take advantage of going to Packapalooza on Hillsborough Street from 2-10pm. Please sign…
Conventional superconductivity emerges for weakly interacting Fermi gases, and its emergence has been studied in mathematical physics. Such conventional superconductors, however, have a very low critical temperature, making them very expensive in applications. Unconventional superconductors, such as cuperates, on the other hand exhibit a very high critical temperature, but we have very little understanding of…
In this talk, I will explore the relationship between a domain's shape and its first Laplace eigenvalue, with emphasis on the domains which minimize, or are more generally critical points, for this eigenvalue, for their given volume.
We will give an introduction to nets of associative algebras over discrete metric spaces, which arise in mathematical physics as axiomatizations of the observables content of quantum field theories over discrete spaces. We will present examples arising naturally from combinatorics and representation theory, and discuss some recent structural results about these objects. Speaker's website: https://www.coreyjonesmath.com/
Malaria is a deadly infectious disease causing over 200 million cases and over half a million deaths each year. It is transmitted through the bite of an infectious Anopheles mosquito. Control methods, primarily focused on affecting the ability of the mosquito to bite or transmit the disease by employing insecticides, have reduced the impact of…
The theory of integral closure of ideals, originating in the early twentieth century with work of Krull, Zariski, Rees, and others, remains a vibrant area of research in algebraic geometry, commutative algebra, and singularity theory. This theory's significance partly stems from its connections with numerical invariants such as multiplicities. During the 1950s, significant advances by…
This Wednesday, September 4th at 6:00pm SUM Club will be hosting a comedy talk on some quirked up (recent) mathematical history! Our esteemed community coordinator, Quill Nebeker, will be presenting on: “That Time We Discovered the Proof for a Major Open Question in Mathematics in a 4chan Post About Anime from 2011” The meeting will be in…
In this talk we will discuss a collection of convolution inequalities for real valued functions on the hypercube, motivated by combinatorial applications. Speaker's website: https://sites.google.com/site/joseramonmadridpadilla/home