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Events happening on April 29, 2014

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Apr. 29, 2014 9am (MATH 350)	PDE/Analysis Alejandro Sarria (CU Boulder) X We discuss a particular class of solutions to 3D Euler which blowup in finite time from smooth initial data. This family of exact solutions has infinite energy and was derived by Peter Constantin. Some qualitative properties of blowup are also addressed. Riccati Blowup in Semibounded Solutions to 3D Euler
Apr. 29, 2014 1pm (MATH 350)	Number Theory Hershy Kisilevsky (Concordia University) X For an elliptic curve $E$ defined over the rational field, $ℚ$ , we will be interested in the variation of the Mordell-Weil groups $E(K)$ as $K$ ranges over finite extensions of $ℚ$ . In particular we will examine the ranks of $E(K)$ (both algebraic and analytic), as $K$ varies and give some of our results and conjectures on the values obtained. Acquiring Algebraic Points on Elliptic Curves
Apr. 29, 2014 1pm (MATH 220)	Grad Algebra/Logic Michael Pinsker (Universite Diderot, Paris) X A function clone on a set D is a set of finitary operations on D which is closed under composition and which contains the projections. Every function clone carries a natural algebraic structure given by the equations that hold in the clone, as well as a natural topological structure given by pointwise convergence. Let P be the function clone consisting of all projections on a two-element set. Given any function clone C on a countably infinite set, we compare the following questions: 1) Is there a homomorphism from C to P? 2) Is there a continuous homomorphism from C to P? These questions have applications in constraint satisfaction. More context will be provided in the subsequent talk in the logic seminar. Decomposing function clones on infinite sets Sponsored by the Meyer Fund
Apr. 29, 2014 2pm (MATH 350)	Lie Theory Jonathan Lamar (CU) X I will be presenting on a paper of Halasi and Palfy in which they prove that for certain pattern subgroups of UT(n,q), the number of conjugacy classes is not given by a polynomial equation in q. Moreover, they also prove that for some pattern groups, the number of conjugacy classes is not given by even a finite set of polynomials in q. This result is related to a famous open problem posed by Graham Higman, who asked if the number of conjugacy classes of UT(n,q) is given by a polynomial in q. Pattern groups whose number of conjugacy classes is not given by a polynomial
Apr. 29, 2014 2pm (MATH 220)	Michael Pinsker (Universite Diderot, Paris) X The Constraint Satisfaction Problem (CSP) of a finite or countable first-order structure S in a finite relational language is the problem of deciding whether a given conjunction of atomic formulas in that language is satisfiable in S. Many classical computational problems can be modelled this way. The study of CSPs involves an interesting combination of techniques from universal algebra, Ramsey theory, and model theory. This talk will present an overview over these techniques as well as some wild conjectures. Introduction to Constraint Satisfaction over infinite structures Sponsored by the Meyer Fund
Apr. 29, 2014 3pm (Math 220)	Algebraic Geometry Samouil Molcho (Brown) X The space of stable log maps of Abramovich-Chen and Gross-Siebert is a central object of study in singular Gromov-Witten theory. In this talk, I will give an explicit combinatorial description of the space of genus 0, 2 pointed stable maps to a toric variety: it is an appropriate enrichment of the Chow Quotient of Kapranov-Sturmfels-Zelevinsky into a toric stack. The idea for this description comes from Morse Theory. This is joint work with William Gillam. Logarithmic Stable Maps as Moduli of Broken Orbits Sponsored by the Meyer Fund

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