# Seminars and Colloquia

## Colloquium

Nov 14

04:00 pm

Exley Science Center Tower ESC 339

一道本不卡免费高清 Speaker: Vic Reiner, University of Minnesota Time and Date: 4:00-5:00 p.m., November 14, 2018 Location: 339 Exley (also available on Zoom) Title: Cyclic Sieving: Old and New Abstract: Cyclic sieving, identified in work with Dennis Stanton and Dennis White, is a happy situation, where counting how many among some objects enjoy cyclic symmetry is as easy as q-counting all of the objects. We will illustrate this with two kinds of examples: old ones that still plague us with only uninsightful proofs, and new ones that have joined our list of favorites. Zoom link: http://smcvt.zoom.us/j/446360634 Zoom tip and further information: http://sites.google.com/view/northeastcombinatoricsnetwork/events/virtual-combinatorics-colloquium

Apr 19

04:20 pm

Exley Science Center Tower ESC 121

一道本不卡免费高清 Rachel Roberts, Washington University Introducing meridional cusps Abstract:I will define taut foliations and branched surfaces in 3-manifolds, anddescribe a search for co-oriented taut foliations using branched surfaces asthe primary tool. This search is inspired by results from Heegaard Floerhomology. This work is joint withCharles Delman.

Apr 12

04:20 pm

Exley Science Center Tower ESC 121

一道本不卡免费高清 Aaron Brown, University of Chicago Recent progress in the Zimmer program Abstract:The Zimmer program refers to a number of questions and conjecturesabout actions of certain discrete groups, namely, lattices in higher-ranksimple Lie groups. The primary example example of a such a group is SL(n,R). In the past few years, there has been significant progress in the Zimmerprogram. In my talk, I will discuss a recent proof of Zimmer's conjecturewhich shows that (cocompact and certain non-uniform) higher-rank lattices donot act on manifolds with low dimension. I will also discuss recentresults and work in progress that classify all possible non-trivial actionsunder certain dynamical or dimension assumptions.

Dec 7

04:20 pm

一道本不卡免费高清Exley Science Center Tower ESC 121

一道本不卡免费高清 Vincent Guingona, Towson Title: Machine learning theory andmodel theory. Abstract: We discuss some basicconcepts in machine learning theory, including concept classes, VC-dimension,VC-density, PAC-learning, and sequence compressions. We then explore therelationship between these concepts and model theory.

Nov 9

04:20 pm

Exley Science Center Tower ESC 121

Speaker: Nadja Hempel, UCLA Mekler constructions in generalized stability Abstract: Given a so called nice graph (no triangles, no squares, for any choiceof two distinct vertices there is a third vertex which is connected to one andnot theother), Mekler considered the 2-nilpotent subgroup generated bythe vertices of the graph in which two elements given by vertices commute ifand only if there is an edge between them. These groups form an interestingcollection of examples from a model theoretic point of view. It was shown thatsuch a group is stable if and only if the corresponding graph is stable andBaudisch generalized this fact to the simple theory context. In a joint workwith Chernikov, we were able to verify this result for k-dependent and NTP_2theories. This leads totheexistence of groups which are(k+1)-dependent but not k-dependent, providing the first algebraic objectswitnessing the strictness of thesehierarchy. Thisis joint work with Artem Chernikov.

Nov 2

04:20 pm

一道本不卡免费高清Exley Science Center Tower ESC 121

一道本不卡免费高清 Jonathan Huang, Wes Title:ZetaFunctions, Witt rings, and a Classical Formula of MacDonald Abstract: Aremarkable formula of MacDonald provides a closed expression for the generatingseries of the Poincar polynomialof the symmetric powers Sym n X of a space X . We show that this formula takes a very nice form when rewrittenin the big ring of Witt vectors W ( [ z ]) of the polynomial ring [ z ]. We then provide some motivation forsimilarly viewing the Hasse-Weil zeta function of varieties over finite fields aselements in the big Witt ring W ( ). In this setting, the zetafunction Z ( X , t ) takes the form ofan Euler-Poincar characteristic.

Oct 19

04:20 pm

Exley Science Center Tower ESC 121

Speaker: Alex Kruckman, Indiana University-Bloomington Title:First-order logic and cologic over a category Abstract: In ordinary first-order logic, each formula comes with a finitevariable context. In order to assign a truth value to the formula, we need aninterpretation of its context: an assignment of the variables to elements of astructure. I will describe a categorical generalization of first-order logic,obtained by replacing the category of finite sets (variable contexts) with any smallcategory C with finite colimits, and replacing arbitrary sets (domains ofstructures) with formal directed colimits from C. I will present a deductivesystem and completeness theorem for this logic, which is related tohyperdoctrines, a notion from categorical logic. Once this categoricalframework is in place, it is easily dualizable. The result is a first-order"cologic", which is well-suited for studying profinite structures interms of their finite quotients; indeed, this was the original motivation. Asparticular examples, I will explain how the framework includes the"cologic" of profinite groups due to Cherlin, Macintyre, and van denDries, and the theories of projective Fraisse limits due to Solecki and Irwin.

Oct 12

04:20 pm

Exley Science Center Tower ESC 121

一道本不卡免费高清 Speaker: James Freitag, University of Illinois-Chicago Title: Algebraicrelations between solutions of Painlev equations Abstract: Painlev equations are families of second order nonlinear differentialequations which were first discovered in the late 19th century, in connectionwith problems in analysis around analytic continuation. Interest in theequations has increased in large part because of connections to numerous othersubjects including random matrix theory, monodromy of linear differentialequations, and diophantine geometry. In this talk, we will describe recentinteractions with model theory which have resulted in the proof of severalconjectures related to transcendence of solutions of Painlev equations.

Oct 5

04:20 pm

一道本不卡免费高清Exley Science Center Tower ESC 121

一道本不卡免费高清 Speaker: Shelly Harvey, Rice University Title: Corank of 3-manifold groups G withH_2(G)=0 Abstract: The corank of a group G, c(G), is the maximal r such that there is asurjective homomorphism from G to a non-abelian free group of rank r. Wenote that for any group G, c(G) is bounded above by b_1(G), the rank of theabelianization of G. For closed surface groups S, we have a furtherrelationship between these two complexities, namely b_1(S) = 2 c(S). It wasasked whether such a relationship exists for 3-manifold groups. In aprevious paper, I showed that there were closed 3-manifold groups G with b_1(G)arbitrarily large but with c(G)=1. It was asked by Michael Freedmanwhether such a statement was known when the group was the group of a 3-dimensionalhomology handlebody. These groups are much more subtle and haveproperties that make them look like a free group so the question becomes muchmore difficult. In fact, all of theprevious techniques used by the author fail. The complete answer to the questionis still unknown. However, we show that there are groups G_m (for all m\geq 2) which are the fundamental group of a 3-dimensional handlebody (inparticular, H_2(G_m)=0) and satisfy the following: b_1(G_m)= m and c(G_m)=f(m)where f(m)=m/2 for m even and f(m)=(m+1)/2 for m odd. This is joint workwith Eamonn Tweedy.

Mar 9

04:20 pm

一道本不卡免费高清Exley Science Center Tower ESC 121

一道本不卡免费高清 Kevin Tucker, University of Illinois - Chicago: An Introduction to F-Signature Abstract: In positive characteristic p > 0, Frobenius splitting methods havelong been used to measure singularities. Although these techniquesoriginally found applications in commutativealgebraandrepresentation theory, in recent years they haveincreased in importance following the discovery of surprising connections tothe singularities of the minimal model program in complex algebraicgeometry. In this talk, I will discuss an invariant governing theasymptotic behavior of F-splittings called the F-signature, together withnumerous examples.

Dec 8

04:20 pm

一道本不卡免费高清Exley Science Center Tower ESC 121

一道本不卡免费高清 Moon Duchin, Tufts: Sprawland other geometric statistics Abstract: I'll define a statistic called the "sprawl" of a metricmeasure space which quantifies the degree of rapid, homogeneous spreading outthat is characteristic of trees. Related statistics come up across geometry,in group theory, in category theory, and in applications from biodiversity togerrymandering. In this talk I'll spend some time on examples from convexgeometry and will try to get to voting applications by the end.

Dec 1

04:20 pm

Exley Science Center Tower ESC 121

Karen Melnick, University of Maryland: Limits of local autommorphisms of geometric structures Abstract: The automorphism group of a rigid geometric structure is a Liegroup. In fact, the local automorphisms form a Lie pseudogroup; thisproperty is often taken as an informal definition of rigid geometricstructure. In which topology is this the case? The classicaltheorems of Myers and Steenrod say that $C^0$ convergence of local isometriesof a smooth Riemannian metric implies $C^\infty$ convergence; in particular,the compact-open and $C^\infty$ topologies coincide on the isometrygroup. I will present joint results with C. Frances in which we prove thesame result for local automorphisms of smooth parabolic geometries, a richclass of geometric structures including conformal and projectivestructures.