Title: 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
Our first ever virtual Lunch and Learn will be on Wednesday, September 30, 2020 at 12:00 p.m. via zoom. We will be talking about Mathematics and Modeling COVID19. Please email awm@ua.edu for the Zoom link and password.
Title: 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
Title: On a structure theorem of doubling weights, Muckenhoupt Ap weights and reverse Holder weights. Abstract: In this talk, I will introduce a way to construct an explicit family of measures on the real line that are p-adic doubling for any finite set of primes, however, not doubling. This part generalizes the work of Boylan,
Dr. 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.
Title: 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
Our first AWM Talk Series event is scheduled on Wednesday, October 7th, 3:30 - 4 PM. The speaker is UA Alumna, Dr. Keisha Cook! Keisha is a postdoctoral researcher at Tulane University. Her research interests include computational biology, statistical analysis and particle tracking. Join us to learn more about her research! Topic: AWM Talk Series
Title: A local-to-global method for inequalities in weighted Sobolev spaces. Abstract: In this talk, we will discuss a certain local-to-global technique with applications to inequalities in weighted Sobolev spaces, such as fractional Poincaré-type inequalities and Korn and conformal Korn inequalities. This technique is based on a certain decomposition of functions that extends the validity of the inequalities
Title: On rationally slice knots Abstract: A knot in the three-sphere is called slice if it bounds a smooth disk in the four-ball. If one only requires the disk to be in a rational homology four-ball, then we say that the knot is rationally slice. We present a rationally slice knot which is not slice even
Title: The Robin problem over irregular domains Abstract: We will discuss the solvability and global regularity theory for the Laplace equation with Robin boundary conditions over classes of irregular domains which include non-Lipschitz domains and domains with fractal boundaries.
The speaker is UA Alumna, Dr. Tania Hazra, an assistant professor at Misericordia University. This talk will discuss some innovative ideas for teaching during Coronavirus pandemic. Topic: AWM Talk Series Part I with Dr. Tanya Hazra Time: Oct 19, 2020 03:30 PM Central Time (US and Canada)
Title: Free Boundary Problem: Challenges and Applications Abstract: There exists a wide range of modern and important physical and Biological phenomena that are described as free boundary problems. The difficulty in solving them stems from the fact that the solution depends on a boundary that evolves in time, at which boundary conditions must be imposed
Title: Abstract Infinite Group Theory in Linear Groups. Abstract: It is a classical result that the commutator subgroup of a group $G$ is finite whenever such is the factor group $G/Z(G)$. In general, this result cannot be reverted: there are (soluble) groups with a finite commutator subgroup but an infinite factor over the centre. However,
Title: On the weak differentiability of the fractional maximal function Abstract: The fractional maximal functions are comparable in Lp size to the Riesz potentials of same order. Its smoothing properties are however more subtle. In this talk, I will discuss Sobolev regularity of fractional maximal functions on the Euclidean n-space as well as on bounded
TITLE: Diffuse interface methods for incompressible two-phase flows ABSTRACT: The diffuse interface (or phase field) theory has emerged in the last decades as a versatile approach to describe the interface dynamics in many problems arising from fluid and solid mechanics, image processing, material sciences and biology. Among many, recent applications are Li-ion batteries and tumor
Title: An Introduction to Cluster Algebras Abstract: Cluster algebras are commutative algebras with a special combinatorial structure. They were introduced in 2002 by Sergey Fomin and Andrei Zelevinsky in the context of canonical bases in Lie theory and have quickly developed deep connections to other areas of mathematics and physics, including combinatorics, representation theory, hyperbolic geometry, elementary
Martha Makowski and Jim Gleason will be hosting a Math Ed get together meeting to answer questions , check in and talk about the research that is going on in the department.