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Events happening on November 12, 2013

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Nov. 12, 2013 10am (MATH 350)	Ulam Pearce Washabaugh X We will describe techniques to solve the forward and inverse scattering problems for the Schrödinger Operator, and then discuss how these can be used to solve the KdV equation. An Introduction to the Inverse Scattering Transform
Nov. 12, 2013 1pm (MATH 220)	Grad Algebra/Logic Heinz Peter Gumm (Philipps-University, Marburg, Germany, and Chapman University, Ora…) X Universal Co-Algebra is a general theory of state based systems, encompassing familiar structures, such as automata, Kripke Structures, dynamical systems, stochastic automata, even topological spaces considered as doubly nondeterministic transition systems. In order to capture and generalize systems with such diverse behaviours, the mathematical language to deal with universal coalgebra is Category theory. The results obtained this way are very concrete: homomorphism theorems, Birkhoff style theorems, classification theorems, and they can be very elegantly derived, using only elementary categorical notions and tools. Universal Co-Algebra is in many ways dual to Universal Algebra, and when translating co-algebraic proofs, one even obtains elegant proofs of universal algebraic results, albeit in a more general setting than that of classical universal algebra. Universal Co-Algebra
Nov. 12, 2013 1pm (MATH 350)	Number Theory Phillip Habegger X Conjectures on unlikely intersections generalize various problems in diophantine geometry such as the Manin-Mumford Conjecture. They originated in work of Bombieri-Masser-Zannier, Pink, and Zilber. Using a point counting result of Pila-Wilkie formulated in the language of o-minimal structures, Zannier devised a new strategy to prove the Manin-Mumford Conjecture. After providing some historical background on unlikely intersections I will explain what an o-minimal structures is. Then I'll describe a possible approach for dealing with higher dimensional unlikely intersections in abelian varieties defined over number fields. This is joint work in progress with Jonathan Pila. Unlikely Intersections and o-Minimal Structures
Nov. 12, 2013 2pm (MATH 350)	Lie Theory Uriya First (Hebrew University) X In short: I will explain how to use bilinear forms to prove theorems of Albert and Saltman about algebras with involution as well as several other related results. In detail: A well-known theorem of Albert states that a central simple algebra A of period 2 in the Brauer group admits an involution of the first kind (i.e. fixing the center). This was generalized by Saltman to Azumaya algebras with the difference that the conclusion is that there is some algebra in the Brauer class of A admitting an involution of the first kind. Albert and Saltman also gave necessary and sufficient conditions for existence of involutions of the second kind (i.e. not fixing the center). Another proof of Saltman's Theorem was later given by Knus, Parimala and Srinivas. I will discuss a new approach to Saltman's Theorem based on bilinear forms. This approach gives a new perspective on the proof of Knus-Parimala-Srinivas and also give rise to further results and generalizations. I shall also explain how to apply this approach to construct Azumaya algebras of period 2without involution. All notions (e.g. Brauer Group, Azumaya algebra) will be defined during the talk. Azumaya Algebras With and Without Involution
Nov. 12, 2013 3pm (MATH 220)	PDE/Analysis Jiahong Wu (Oklahoma State University) X The Boussinesq equations concerned here model geophysical flows such as atmospheric fronts and ocean circulations. Mathematically the 2D Boussinesq equations serve as a lower-dimensional model of the 3D hydrodynamics equations. In fact, the 2D Boussinesq equations retain some key features of the 3D Euler and the Navier-Stokes equations such as the vortex stretching mechanism. The global regularity problem on the 2D Boussinesq equations with partial or fractional dissipation has attracted considerable attention in the last few years. This talk reviews recent results on various cases of partial dissipation and presents most recent developments on the 2D Boussinesq equations with partial and fractional dissipation. Recent developments on the 2D Boussinesq equations with partial dissipation
Nov. 12, 2013 3pm (MATH 350)	Algebraic Geometry Qile Chen (Columbia) X The theory of stable log maps are developed for studying the degeneration of Gromov-Witten invariants. In this talk, I will introduce another interesting application of stable log maps to classicalbirational geometry ---- We construct very free rational curves on Fano complete intersections in projective spaces over an algebraically closed field of arbitrary characteristics. This a joint work with Yi Zhu. Very free rational curves on Fano complete intersections

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