Events
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SAS 4104Kazufumi Ito, NC State, Optimal control of sate constrained PDEs system with Spars controls
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…
Mette Olufsen, NC State, How mathematical techniques can be used to better understand cardiovascular dynamics in health and disease
SAS 2102Dating 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…
Jonathan Campbell, Duke University, The Scissors Congruence Problem and the Algebraic K-theory of the Complex Numbers
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…
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SAS 4104Yulong Lu, Duke University, Understanding and accelerating statistical sampling algorithms: a PDE perspective
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…
Ricky Liu, NC State, RSKy Business
SAS 2102The 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.
Pratik Misra, NC State, Bounds on the expected size of the maximum agreement subtree
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…
Jean-Pierre Fouque, University of California Santa Barbara, Stochastic Games with Delay: a Toy Model
Park Shops 200Motivated 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…
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Pedro Aceves Sanchez, NC State, Emergence of Vascular Networks
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…
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SAS 4104Nathan Reading, NC State, Regular Polytopes and Tessellations: Why life is more interesting in low dimension
SAS 2102Polytopes (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…
Christian Smith, NC State, The Algebra of “up-operators” for Young’s Lattice and Bruhat Order on S_n
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…
Emily Gunawan, University of Connecticut, Cambrian combinatorics on quiver representations
Let Q be an orientation of a type A Dynkin diagram. An eta map corresponding to Q is a surjection from the weak order on permutations to a Cambrian lattice (of triangulations of a polygon). We give a new geometric way to construct the Auslander-Reiten quiver of the quiver representations rep(Q). We use it to naturally define…
Donald Sheehy, NC State, On the Cohomology of Impossible Figures, Revisited
The Penrose triangle, also known as the impossible tribar is an icon for cohomology. It is literally the icon for Cech cohomology on Wikipedia. The idea goes back to a paper by Roger Penrose in 1992, but was first reported by Penrose several years earlier. There, he shows how the impossibility of the figure depends…