# Category Archives: Seminars

## Bruno Braga: On the rigidity of uniform Roe algebras of coarse spaces

Place: Fields Institute (Room 210)

Date: March 2 , 2018 (13:30-15:00)

Speaker: Bruno Braga

Title: On the rigidity of uniform Roe algebras of coarse spaces.

Abstract: (joint with Ilijas Farah) Given a coarse space (X,E), one can define a $C^*$-algebra $C^∗_u(X)$ called the uniform Roe algebra of (X,E). It has been proved by J. \v{S}pakula and R. Willet that if the uniform Roe algebras of two uniformly locally finite metric spaces with property A are isomorphic, then the metric spaces are coarsely equivalent to each other. In this talk, we look at the problem of generalizing this result for general coarse spaces and on weakening the hypothesis of the spaces having property A.

## Adam Bartoš: Compactifiable classes and Borel complexity up to the equivalence

The seminar meets on Wednesday March 7th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Adam Bartoš — Compactifiable classes and Borel complexity up
to the equivalence
We discuss the notion of compact composition of a class of metrizable
compacta, and a general question of compactifiability of a given class.
This is connected to the Borel complexity of subsets of the hyperspace
of all metrizable compacta, up to the equivalence of classes.

## Jacek Tryba: Homogeneity of ideals

Tuesday, March 6, 2018, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Jacek Tryba (University of Gdansk)

Title: Homogeneity of ideals

Abstract:

The homogeneity family of the ideal $\mathcal{I}$ is a family of subsets such that the restriction of $\mathcal{I}$ to this subset is isomorphic to $\mathcal{I}$.
We say that an ideal $\mathcal{I}$ is homogeneous if all $\mathcal{I}$-positive sets belong to the homogeneity family of $\mathcal{I}$. We investigate basic properties of this notion, give examples of homogeneous ideals and present some applications to ideal
convergence.
Moreover, we present connections between the homogeneity families and the notion of bi-$\mathcal{I}$-invariant functions introduced by Balcerzak, Głąb and Swaczyna and give answers to several questions related to this topic.

## Rick Statman: Completeness of BCD for an operational semantics; forcing for proof theorists II

Mathematical logic seminar – Feb 27 2018
Time:   3:30pm – 4:30 pm

Room:   Wean Hall 8220

Speaker:        Rick Statman
Department of Mathematical Sciences
CMU

Title:  Completeness of BCD for an operational semantics; forcing for proof theorists II

Abstract:

Intersection types provide a type discipline for untyped λ-calculus. The formal theory for assigning intersection types to lambda terms is BCD (Barendregt, Coppo, and Dezani). We show that BCD is complete for a natural operational semantics. The proof uses a
primitive forcing construction based on Beth models (similar to Kripke models).

## Jan Grebik: Applications of topological dynamics to graphons

The seminar meets on Wednesday February 28th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Jan Grebik — Applications of topological dynamics to graphons
We show that the question about the existence of a Borel or continuous
lift for graphons has its counterpart in topological dynamics. We
present the optimal result in the general setting and then translate it
back to the original problem.

## Frank Tall: Co-analytic spaces, K-analytic spaces, and definable versions of Menger’s conjecture

Place: Fields Institute (Room 210)

Date: February 23 , 2018 (13:30-15:00)

Speaker: Frank Tall

Title: Co-analytic spaces, K-analytic spaces, and definable versions of Menger’s conjecture

Abstract: We continue the study of K-analytic and related spaces started last time, especially the connections between descriptive set theory as presented by Rogers and Jayne, and generalized metric spaces. We shall mention a number of unsolved problems and also give applications to productively Lindelof spaces and to topological groups.

## Sibylle Schwarz: Many-valued logic, Automata and Languages

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 21 February 2018, 17:00 hrs

Room: S17#04-06, Department of Mathematics, NUS

Speaker: Sibylle Schwarz

Title: Many-valued logic, Automata and Languages.

URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

Abstract:
In 1960, Buechi, Elgot, Trakhtenbrot discovered a correspondence
between finite automata and monadic second order logic on words:
A language of nonempty words is regular if and only if it is
MSO-definable. Many-valued logics with truth values from MV-algebras
and weighted automata with weights from semirings are generalizations
of classical two-valued logics and finite automata, respectively.
In this talk, I give some examples of corresponding MV-algebras
and semirings and present translations between many-valued
MSO-formulae and weighted automata that define the same language.

## James Cummings: Some strong chain conditions

Mathematical logic seminar – Feb 20 2018
Time:     3:30pm – 4:30 pm

Room:     Wean Hall 8220

Speaker:         James Cummings
Department of Mathematical Sciences
CMU

Title:     Some strong chain conditions

Abstract:

One of the basic facts in forcing is that a finite support iteration of ccc forcing is ccc. This underlies (for example) the consistency proof for Martin’s Axiom. In general an iteration of κ-closed κ+-cc forcing with <κ-support fails to be κ+-cc, and we need strngthened forms of the chain condition. I will discuss some of these strong chain conditions and the corresponding iteration theorems.

## Chris Kapulkin: Homotopy Type Theory and internal languages of higher categories

Thursday, February 22, 2018, from 4 to 5:30pm
East Hall, room 3088

Speaker: Chris Kapulkin (University of Western Ontario)

Title: Homotopy Type Theory and internal languages of higher categories

Abstract:

Homotopy Type Theory (or HoTT) is an approach to foundations of mathematics, building on the homotopy-theoretic interpretation of type theory. In addition to its foundational role, HoTT has been speculated to be the internal language of higher toposes in the sense of Joyal and Lurie.
This talk will be an introduction to HoTT, explaining its main ideas and presenting one way in which the connection between type theory and higher categories can be made precise.

## Will Brian: Autohomeomorphisms of ω∗ : the quotient relation

Place: Fields Institute (Room 210)

Date: February 16, 2018 (13:30-15:00)

Speaker: Will Brian

Title: Autohomeomorphisms of ω∗ : the quotient relation

Abstract: Given two autohomeomorphisms f and g of N*, we say that f is a quotient of g when there is a continuous surjection Q from N* to N* such that Qg = fQ. In other words, f is a quotient of g if it is the “continuous image” of g, in the appropriate sense.

I have been investigating this relation, and will present some of the results of that investigation in my talk. For example, under CH: there are many universal autohomeomorphisms (an autohomeomorphism is universal if everything else is a quotient of it); the quotient relation has uncountable chains and antichains; there is an exact description of the quotients of a given trivial map. Under OCA+MA the picture is still murky: for example, there is a jointly universal pair of autohomeomorphisms (meaning everything else is a quotient of one or the other), but I do not know if there is a single universal automorphism. I will sketch some of these results and include several open questions.