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Talk_id	Date	Speaker	Title
14372	Monday 8/20 11:00 AM	Soumyashant Nayak, University of Pennsylvania	Analyticity in Operator Algebras New Window Analysis and PDE Speaker: Soumyashant Nayak, University of Pennsylvania Title: Analyticity in Operator Algebras Date: 08/20/2018 Time: 11:00 AM - 12:00 PM Place: C517 Wells Hall The title of this talk is borrowed from a seminal paper by Arveson discussing non-commutative analogues of the Hardy space H^∞(T) via the so-called subdiagonal algebras. Subdiagonal algebras are a family of non-self-adjoint operator algebras which give a common perspective to the study of some triangular operator algebras (for example, the algebra of block upper triangular matrices in M_n(C)), Dirichlet function algebras, etc. The first part of the talk will be about a non-commutative version of inner-outer factorization in finite maximal subdiagonal algebras. We will then discuss a proof of a version of Jensen's inequality in this setting which relates to some classical results by Szegö.
15401	Wednesday 9/12 4:00 PM	Alex Waldron, MSU	Yang-Mills flow in dimension four New Window Analysis and PDE Speaker: Alex Waldron, MSU Title: Yang-Mills flow in dimension four Date: 09/12/2018 Time: 4:00 PM - 4:50 PM Place: C517 Wells Hall Among the classical geometric evolution equations, YM flow is the least nonlinear and best behaved. Nevertheless, curvature concentration is a subtle problem when the base manifold has dimension four. I'll discuss my proof that finite-time singularities do not occur, and briefly describe the infinite-time picture. This talk will be more analytic and contains <50% overlap with my talk last Thursday.
14348	Wednesday 9/19 4:10 PM	Richard Kollar, Comenius University, Bratislava, Slovakia	Krein signature - three unexpected lessons New Window Analysis and PDE Speaker: Richard Kollar, Comenius University, Bratislava, Slovakia Title: Krein signature - three unexpected lessons Date: 09/19/2018 Time: 4:10 PM - 5:00 PM Place: C517 Wells Hall Krein signature is an algebraic quantity characterizing purely imaginary eigenvalues of linearized Hamiltonian systems. Instabilities growing from a stable state in these systems are caused by Hamiltonian-Hopf bifurcations, i.e. events when two purely imaginary eigenvalues collide and split off the imaginary axis. The necessary condition for such an event is that the colliding eigenvalues must have mixed signature. In the talk we present three elegant results related to Krein signature - graphical Krein signature and its use to simplify proofs, a connection to stability in general extended systems, and ability to characterize the nature of the eigenvalue collisions directly from the reduced dispersion relation.
15389	Wednesday 10/3 4:10 PM	N. K. Nikolski, University of Bordeaux	V.Ya.Kozlov's completeness problem New Window Analysis and PDE Speaker: N. K. Nikolski, University of Bordeaux Title: V.Ya.Kozlov's completeness problem Date: 10/03/2018 Time: 4:10 PM - 5:00 PM Place: C517 Wells Hall In 1948-1950, V.Ya.Kozlov (1914-2007) stated a series of interesting geometric properties of dilated systems D(f)= {f(kx): k= 1,2,...} in the spaces L^p(0,1). Since that, no proofs were published. In particular, for a Rademacher-Haar-Walsh type generator f= 2-periodic odd extension of the indicator function of (0,a), 0<a<1, the system D(f) was claimed to be complete/incomplete for many particular values of a. We prove all Kozlov's statements and several new, as well as discuss other geometric properties of D(f).
15390	Wednesday 10/10 4:10 PM	N. K. Nikolski, University of Bordeaux	Dilated systems and multivariable analysis New Window Analysis and PDE Speaker: N. K. Nikolski, University of Bordeaux Title: Dilated systems and multivariable analysis Date: 10/10/2018 Time: 4:10 PM - 5:00 PM Place: C517 Wells Hall Geometric L^2(0,1) properties of dilated function systems D(f)= {f(kx): k= 1,2,...} are discussed, as completeness, Riesz basis property, etc. (Completeness of D(f) for f(x)= 1/x-[1/x] is equivalent to the Riemann Hypothesis). The Bohr's lift techniques permit to explain (all) known results and show some new, as well as to discuss open problems.
15406	Wednesday 10/24 4:10 PM	Maxim Gilula, MSU	l^2 decoupling with vanishing curvature New Window Analysis and PDE Speaker: Maxim Gilula, MSU Title: l^2 decoupling with vanishing curvature Date: 10/24/2018 Time: 4:10 PM - 5:00 PM Place: C517 Wells Hall I will discuss recent progress on decoupling for curves with vanishing curvature.
15391	Wednesday 10/31 4:10 PM	Irina Holmes, MSU and Texas A&M	Bellman and Bollobas Functions New Window Analysis and PDE Speaker: Irina Holmes, MSU and Texas A&M Title: Bellman and Bollobas Functions Date: 10/31/2018 Time: 4:10 PM - 5:00 PM Place: C517 Wells Hall No abstract available.
15392	Wednesday 11/14 4:10 PM	Dominique Maldague, UC Berkeley	TBA New Window Analysis and PDE Speaker: Dominique Maldague, UC Berkeley Title: TBA Date: 11/14/2018 Time: 4:10 PM - 5:00 PM Place: C517 Wells Hall No abstract available.

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Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824
Phone: (517) 353-0844
Fax: (517) 432-1562

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