Applying for Graduate Research Fellowships
Speaker: Seth Sullivant This presentation will explain the ins and outs of applying for graduate research fellowships, with special emphasis on the NSF graduate research fellowship.
Speaker: Seth Sullivant This presentation will explain the ins and outs of applying for graduate research fellowships, with special emphasis on the NSF graduate research fellowship.
Modular tensor categories are rich mathematical structures. They are important in the study of 2D conformal field theory, arising as categories of modules for rational vertex operator algebras. The orbifold construction A-> A^{G} for a finite group G is a fundamental method for producing new theories from old. In the case the orbifold theory is also rational, the construction of…
We will talk about Kronheimer and Mrowka’s knot concordance invariant, $s^\sharp$. We compute the invariant for various knots. Our computations reveal some unexpected phenomena, including that $s^\sharp$ differs from Rasmussen's invariant $s$, and that it is not additive under connected sums. We also generalize the definition of $s^\sharp$ to links by giving a new characterization…
In this talk we discuss a point-wise state constraint problem for a general class of PDEs optimal control problems and sparsity optimization. We use the penalty formulation and derive the necessary optimality condition based on the Lagrange multiplier theory.The existence of Lagrange multiplier associated with the point-wise state constraint as a measure is established. Also we…
Dating back to the 1600s modeling has been used to study cardiovascular dynamics enabling scientist to answer essential questions. In fact, todays knowledge that the cardiovascular system is circulating was first discovered via a mathematical model. In this talk I will discuss the role mathematical analysis has played in cardiovascular physiology and how we use…
In this talk I'll explain a surprising relationship between the objects in the title. Two n-dimensional polytopes, $P$, $Q$ are said to be scissors congruent if one can cut $P$ along a finite number of hyperplanes, and re-assemble it into $Q$. The scissors congruence problem asks: when can we do this? what obstructs this? In…
A fundamental problem in Bayesian inference and statistical machine learning is to efficiently sample from probability distributions. Standard Markov chain Monte Carlo methods could be prohibitively expensive due to various complexities of the target distribution, such as multimodality, high dimensionality, large datesets, etc. To improve the sampling efficiency, several new interesting ideas/methods have recently been proposed in the community…
The Robinson-Schensted-Knuth (RSK) correspondence is an important combinatorial bijection that associates to any permutation a pair of objects called standard Young tableaux. We will describe this correspondence in detail and discuss some interesting connections to combinatorics, algebra, and geometry. This talk will assume no background and will be accessible to all undergraduates.
Rooted binary trees are used in evolutionary biology to represent the evolution of a set of species where the leaves denote the existing species and the internal nodes denote the unknown ancestors. Maximum agreement subtree is used as a measure of discrepancy between two trees. In this talk, I will define the notion of "maximum…
Motivated by modeling borrowing and lending between banks, we start by illustrating systemic risk with a toy model of diffusions processes coupled through their drifts. We then show that such a simplistic model is in fact a Nash equilibrium of a Linear-Quadratic differential game. In order to take into account clearing debt obligations a delay…
All of the math department staff relevant for graduate students will be here to tell you what they do and answer your pressing questions.
he emergence of vascular networks is a long-standing problem which has been the subject of intense research in the past decades. One of the main reasons being the widespread applications that it has in tissue regeneration, wound healing, cancer treatment, etc. The mechanisms involved in the formation of vascular networks are complex and despite the vast amount of research devoted to it, there are still…
Polytopes (also known in dimensions zero through three as "points", "line segments", “polygons", and “polyhedra") have been objects of interest to mathematicians throughout the recorded history of mathematics. Most notably, the five Platonic solids were probably known at least a thousand years before Plato. Regular polytopes are "as symmetric as possible" in a sense that…
Let be a free associative algebra over generated by for in some indexing set and let be a poset. For and we define an action of on (the complex vector space with basis ) in a way such that either annihilates or sends it to where covers and we extend multiplicatively and linearly. Let be the two-sided ideal which annihilates all elements of . We characterize when is Young's Lattice and we discuss the…