College of Liberal Arts and Sciences

# Department of Mathematics

## All Seminars

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Kevin's Test for Scheduling

Title:
Seminar Framework : Testing
Speaker:
Time: Wednesday, March 21, 2018 at 8:00 am
Place: MONT 313

Algebra Seminar

Title: The origin of pictures
Speaker: Kiyoshi Igusa (Brandeis University)
Time: Wednesday, March 21, 2018 at 11:15 am
Place: MONT 313Abstract: Gordana Todorov, Jerzy Weyman, Kent Orr and I are working on a book about pictures'' which have gained renewed attention because they are equivalent to scattering diagrams''. This talk is about very old work that I did to introduce pictures and their relation to the cohomology of $\mathrm{GL}(n,\mathbb Z)$. In particular, I will discuss the pictures below (from our book!) and their relationship to $H^3(\mathrm{GL}(n,\mathbb Z),\mathbb Z/2)$. The algebraic side of this story is a fun topic. The cohomology class which detects the exotic element'' of $K_3(\mathbb Z)$ is the degree 3 class which counts the number of times (modulo 2) that commutativity of addition is used to prove that matrix multiplication is associative! This is an old result (about the obstruction to right distributivity in left near-rings) which I am happy to present in a new light.

Physics Learning Seminar

Title: Tensor networks for open quantum systems and evolution (RESCHEDULED TO FRIDAY)
Speaker: Arthur Parzygnat (University of Connecticut)
Time: Wednesday, March 21, 2018 at 4:00 pm
Place: MONT 214Abstract: We will describe a graphical calculus used to simplify and unify many constructions for the evolution of open quantum systems. Dynamics on a closed system is described by a unitary map. Under suitable conditions, the induced dynamics on a subsystem is described by a completely positive map. This dynamics can be interpreted as the effect of an environment on the subsystem. We will use the graphical calculus to derive an explicit formula for this dynamics providing one motivation for the study of completely positive maps.

UConn Math Club

Title: Using Linear Algebra in Data Science [CANCELED]
Speaker: Matt Lamoureux (Travelers)
Time: Wednesday, March 21, 2018 at 5:45 pm
Place: MONT 321

Discrete Mathematics and Statistical Mechanics

Title: Combinatorics of the 2-ASEP on a ring
Seminar Framework : Reading Group
Speaker: Olya Mandelshtam (Brown University)
Time: Thursday, March 22, 2018 at 2:30 pm
Place: MONT 214Abstract: The two-species asymmetric simple exclusion process (2-ASEP) on a ring is a Markov chain on Z/nZ with each site either vacant or occupied by one of two classes of particles, and whose dynamics are dictated by parameter q: particles can hop right at rate 1 or left at rate q. At q=0, the stationary probabilities of the states of the 2-ASEP can be described by multiline queues of Ferarri and Martin. We show a new combinatorial description of these probabilities in terms of certain cylindric tableaux which are in bijection with the multiline queues. We then extend this result for general q, which furthermore gives a combinatorial formula for certain non-symmetric Macdonald polynomials and proves a positivity conjecture in some special cases. This talk is based on ongoing work with Sylvie Corteel (Université Paris-Diderot) and Lauren Williams (Berkeley).

Physics Learning Seminar

Title: Tensor networks for open quantum systems and evolution
Speaker: Arthur Parzygnat (University of Connecticut)
Time: Friday, March 23, 2018 at 11:15 am
Place: MONT 313Abstract: We will describe a graphical calculus used to simplify and unify many constructions for the evolution of open quantum systems. Dynamics on a closed system is described by a unitary map. Under suitable conditions, the induced dynamics on a subsystem is described by a completely positive map. This dynamics can be interpreted as the effect of an environment on the subsystem. We will use the graphical calculus to derive an explicit formula for this dynamics providing one motivation for the study of completely positive maps. More information including references can be found at https://arthur-parzygnat.uconn.edu/physics-learning-seminar/schedule/Comments: Note the different room

Analysis and Probability Seminar

Title: Densely defined non-closable curl on the Mackay-Tyson-Wildrick carpets
Speaker: Alexander Teplyaev (University of Connecticut)
Time: Friday, March 23, 2018 at 1:30 pm
Place: MONT 414Abstract: The talk will discuss the possibly degenerate behavior of the exterior derivative operator defined on 1-forms on metric measure spaces. The main examples we consider are the non self-similar Sierpinski carpets recently introduced by Mackay, Tyson and Wildrick. Although topologically one-dimensional, they have positive two-dimensional Lebesgue measure and carry nontrivial 2-forms. We prove that in this case the curl operator (and therefore also the exterior derivative on 1-forms) is not closable, and that its adjoint operator has a trivial domain. This is a joint work with Michael Hinz.

Cluster Algebras Seminar

Title: no seminar
Speaker:
Time: Friday, March 23, 2018 at 3:00 pm
Place: MONT 313

Analysis Learning Seminar

Title: An Introduction to Rectifiable Sets and Measures
Speaker: Lisa Naples (University of Connecticut)
Time: Friday, March 23, 2018 at 3:30 pm
Place: MONT 314Abstract: Geometric Measure Theory uses measure theoretic techniques to classify structural properties of sets. A set in Euclidean space can be classified by its Hausdorff dimension, but even sets of a fixed dimension can have drastically different structures. In this talk I will introduce the notion of rectifiability as a structural property of sets, and describe a classification theorem for rectifiable sets of integer dimension. I will end by discussing some more recent extensions to rectifiability of measures.