Math Department
Colloquium – Polona Durcik, California Institute of Technology
346 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesApplied Math Seminar – Toai Luong (University of Alabama)
346 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: Minimizers for the Cahn-Hilliard energy functional under the Dirichlet boundary conditions Abstract: We study the minimizers for the Cahn-Hilliard energy functional with a symmetric quartic double-well potential and under the Dirichlet boundary conditions. Using the Nehari manifold method and connecting it to the eigenvalue problem for the negative Laplacian with the homogeneous boundary condition, we prove that if the boundary value is
Analysis Seminar – Vjekoslav Kovac (University of Zagreb, Croatia and Georgia Tech)
346 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: A Szemeredi-type theorem for subsets of the unit cube. Abstract: We are interested in arithmetic progressions in positive measure subsets of ^d. After a counterexample by Bourgain, it seemed as if nothing could be said about the longest interval formed by sizes of their gaps. However, Cook, Magyar, and Pramanik gave a positive result
Analysis Seminar – José Luis Luna Garcia (University of Missouri)
ZoomTitle: Critical Perturbations and Solvability for Elliptic Equations Abstract: In this talk we will present recent results concerning solvability of certain Boundary Value Problems associated to a general linear second order elliptic equation, under the assumption that the equation is close, in some critical Lebesgue spaces for the coefficients, to an equation for which solvability
Analysis Seminar – John Hoffman (University of Missouri)
ZoomTitle: Regular Lip(1,1/2) Approximation of Parabolic Hypersurfaces Abstract: A classical result of David and Jerison states that a regular, n-dimensional set in R^{n+1} satisfying a two sided corkscrew condition is quantitatively approximated by Lipschitz graphs. After reviewing this result, we will discuss some recent advances in extending this result to the parabolic setting. The proofs
Analysis Seminar – Bruno Poggi (University of Minnesota)
ZoomTitle. Additive and scalar-multiplicative Carleson perturbations of elliptic operators on domains with low dimensional boundaries. Abstract. At the beginning of the 90s, Fefferman, Kenig and Pipher (FKP) obtained a rather sharp (additive) perturbation result for the Dirichlet problem of divergence form elliptic operators. Without delving into details, the point is that if the (additive)
Colloquium – John Baldwin (Boston College)
ZoomTitle: Floer homology and the fundamental group Abstract: The most important invariant of a 3-manifold is its fundamental group. One of the most fruitful approaches to understanding the fundamental group is to study its homomorphisms into simpler groups. SU(2) is an especially convenient choice of target because it is one of the simplest non-abelian Lie
Algebra/Topology Seminar – Honghao Gao (Michigan State University)
ZoomTitle: Legendrian invariants, Lagrangian fillings and cluster algebras Abstract: Classifications of Legendrian knots and their exact Lagrangian fillings are central questions in low-dimensional contact and symplectic topology. Recent development suggests that one can use cluster seeds to distinguish exact Lagrangian fillings. It requires a filling-to-cluster functoriality over a moduli space of Legendrian invariants. This invariant
Colloquium – Mariel Vazquez (University of California at Davis)
ZoomDr. Mariel Vazquez Title: Understanding viruses using topological methods Abstract: For the last 25 years I have studied the effects of DNA packaging as well as the action of DNA binding enzymes responsible for important cellular processes such as DNA replication, or transcription of DNA into RNA.
Algebra/Topology Seminar – Dan Rutherford (Ball State University)
ZoomTitle: Normal rulings, augmentations, and the colored HOMFLY-PT polynomial Abstract: Normal rulings are certain decompositions of front diagrams of Legendrian links in $R^3$ that were discovered independently by Chekanov & Pushkar and Fuchs in the context of generating families and augmentations of the Legendrian DG-algebra respectively. They can be used to define combinatorial invariants of