Math Department
https://wp0.vanderbilt.edu/math
College of Arts and Science | Vanderbilt UniversityThu, 21 Nov 2019 19:00:15 +0000en-UShourly1https://wordpress.org/?v=4.9.8146940276Talk Title TBA
https://wp0.vanderbilt.edu/math/2019/11/talk-title-tba-342/
Thu, 21 Nov 2019 19:00:15 +0000https://wp0.vanderbilt.edu/math/?p=96209620Hierarchically Hyperbolic Groups: An Introduction
https://wp0.vanderbilt.edu/math/2019/11/talk-title-tba-331/
Wed, 20 Nov 2019 21:10:50 +0000https://wp0.vanderbilt.edu/math/?p=9343Hierarchically hyperbolic spaces provide a uniform framework for working with many important examples, including mapping class groups, right angled Artin groups, Teichmuller space, most cubulated groups, and others. In this talk I’ll provide an introduction to studying groups and spaces from this point of view, both describing new tools to use to study these groups and applications of those results. This talk will include joint work with Mark Hagen and Alessandro Sisto.
]]>9343Graduate Student Tea
https://wp0.vanderbilt.edu/math/2019/11/graduate-student-tea-87/
Wed, 20 Nov 2019 21:30:11 +0000https://wp0.vanderbilt.edu/math/?p=96479647Probabilistic Methods in Combinatorics
https://wp0.vanderbilt.edu/math/2019/11/9231/
Tue, 19 Nov 2019 23:00:19 +0000https://wp0.vanderbilt.edu/math/?p=9231Typically, probability theory deals with things which are uncertain on the very ground level. Of course, to struggle with uncertainty is harder, but what can we do? How much simpler would things be if only our objects and actions were clearly determined. Or would they? Surprisingly, it turns out that if our objects are by no means indeterminate, but still complicated enough, it might be convenient to study them as if they were probabilistic. Think of it as saying “whatever” at some point in an argument, but in a strictly mathematical way. In this talk, we will consider some simple examples where these methods can be fruitfully applied.
]]>9231A Full Description of Finite Commutative Idempotent Involutive Residuated Lattices
https://wp0.vanderbilt.edu/math/2019/11/a-full-description-of-finite-commutative-idempotent-involutive-residuated-lattices/
Mon, 18 Nov 2019 22:30:05 +0000https://wp0.vanderbilt.edu/math/?p=9643An involutive residuated lattice is an algebra (A,v,*,~,-,0) such that (A,v) is a semilattice, (A,*) is a semigroup and x <= y if and only if -y*x <= 0 if and only if x*~y <= 0 where <= is the semilattice order. It is commutative if x*y = y*x holds and idempotent if x*x=x holds for all x,y in A. In joint research with Olim Tuyt (University of Bern) and Diego Valota (University of Milan) we have obtained a description of all finite commutative idempotent involutive residuated lattices. The multiplicative order of these algebras is a distributive semilattice that is a disjoint union of Boolean algebras, with involution as complementation within each Boolean algebra. The top elements of the Boolean algebras form a distributive lattice, and given this family of Boolean algebras indexed by the distributive lattice, there is an algorithm for reconstructing the original residuated lattice. We give an example of an infinite one-generated commutative idempotent involutive residuated lattice, hence this variety is not locally finite. We will also discuss possible extensions of the structural description to commutative idempotent involutive posets (ongoing research with Melissa Sugimoto, Chapman University). All idempotent involutive posets with up to 16 elements are commutative, and we present some evidence that this may be true for all finite models.
]]>9643Free Stein Irregularity and Dimension
https://wp0.vanderbilt.edu/math/2019/11/talk-title-tba-320/
Fri, 15 Nov 2019 21:10:39 +0000https://wp0.vanderbilt.edu/math/?p=9258Given an n-tuple $X$ of non-commutative random variables, its free Stein discrepancy relative to the semicircle law (the non-commutative analogue of classical Stein discrepancy relative to the Gaussian distribution) measures how “close” the distribution of $X$ is to the semicircle law. By considering free Stein discrepancies relative to a broader class of laws, one can define a quantity called the free Stein irregularity. I will discuss this quantity and show how it can be related to other free probabilistic quantities such as the free Fisher information and the non-microstates free entropy dimension. I will also show how it can be easily computed for a number of interesting examples. This is based on joint work with Ian Charlesworth.
]]>9258Large Time Behavior of the Fractional Porous Medium Equation on Riemannian Manifolds via Fractional Logarithmic Sobolev Inequalities
https://wp0.vanderbilt.edu/math/2019/11/talk-title-tba-328/
Fri, 15 Nov 2019 21:10:00 +0000https://wp0.vanderbilt.edu/math/?p=9435In 1995, Carlen and Loss proposed a novel approach to study the asymptotics the 2–D Navier–Stokes equation by using a Logarithmic Sobolev inequality. Later, this idea was adopted by Bonforte and Grillo to study the asymptotics of the Porous Medium Equation. In this talk, I will discuss how to derive various Sobolev type inequality involving fractional Laplacian. Then I will use these inequalities to study the smooth effect and asymptotic behavior of the Fractional Porous Medium Equation on complete Riemannian manifolds.
]]>9435Invariants of Rings via Equivariant Homotopy
https://wp0.vanderbilt.edu/math/2019/11/invariants-of-rings-via-equivariant-homotopy/
Thu, 14 Nov 2019 21:10:39 +0000https://wp0.vanderbilt.edu/math/?p=9594Algebraic K-theory is an invariant of rings which illustrates a fascinating interplay between algebra and topology. Defined using topological tools, this invariant has important applications to algebraic geometry, number theory, and geometric topology. One fruitful approach to computing algebraic K-theory uses equivariant homotopy theory, a branch of algebraic topology which studies topological objects with a group action. In this talk I will give an introduction to algebraic K-theory and its applications, and talk about modern methods to compute algebraic K-theory.
]]>9594The Baum-Connes Correspondence for the Pure Braid Group on Four Strands
https://wp0.vanderbilt.edu/math/2019/11/talk-title-tba-327/
Wed, 13 Nov 2019 21:10:02 +0000https://wp0.vanderbilt.edu/math/?p=9298We calculate the left-hand side and the right-hand side of the Baum-Connes correspondence for the pure braid group on four strands, each side relying on different techniques. This is joint work with Sara Azzali, Sarah Browne, Maria Paula Gomez Aparicio, and Hang Wang.
]]>9298Graduate Student Tea
https://wp0.vanderbilt.edu/math/2019/11/graduate-student-tea-86/
Wed, 13 Nov 2019 21:30:01 +0000https://wp0.vanderbilt.edu/math/?p=96359635