# Seminars and Colloquia

## Colloquium

Nov 14

04:00 pm

Exley Science Center Tower ESC 339

Apr 19

04:20 pm

Exley Science Center Tower ESC 121

Apr 12

04:20 pm

Exley Science Center Tower ESC 121

Dec 7

04:20 pm

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

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

Oct 5

04:20 pm

Mar 9

04:20 pm

Dec 8

04:20 pm

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.

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