## David Fernandez Breton: Partition theorems on uncountable abelian groups

Place: Fields Institute (Room 210)

Date: April 27, 2018 (13:30-15:00)

Speaker: David Fernandez Breton

Title: Partition theorems on uncountable abelian groups

Abstract:

In the past two years, a number of Ramsey-theoretic results concerning the additive structure of uncountable abelian groups have been investigated by diverse subsets of the set {Komjáth, Rinot, D. Soukup, W. Weiss, myself} (among others). From Ramsey results generalizing Hindman’s theorem for certain groups and colourings, to anti-Ramsey statements asserting the existence of ”rainbow colourings” for sets of finite sums, I plan to provide a panoramic overview of this exciting line of research, and point towards possible future lines of enquiry.

## Filippo Calderoni – The bi-embeddability relation for countable abelian groups

Talk held by Filippo Calderoni (Università di Torino, Italy and Politecnico di Torino, Italy) at the KGRC seminar on 2018-04-26.

Abstract: We analyze the Borel complexity of the bi‑embeddability relation for different classes of countable abelian groups. Most notably, we use the Ulm theory to prove that bi‑embeddability is incomparable with isomorphism in the case of p‑groups, and torsion groups. As I will explain, our result contrasts the arguable thesis that the bi‑embeddability relation on countable abelian p‑groups has strictly simpler complete invariants than isomorphism.

This is joint work with Simon Thomas.

# Set-Theoretic Topology and Topological Algebra

International Conference Set-Theoretic Topology and Topological Algebra in honor of professor Alexander Arhangelskii on his 80-th birthday

Professor Alexander Vladimirovich Arhangelskii more than forty-five years works at the Faculty of Mechanics and Mathematics, of which over thirty years in the position of professor. A.V. Arhangelskii is a pupil of Academician P.S. Alexandroff, who, together with P.S. Uryson founded the Russian (Soviet) topological school. And to this day the Russian topological school is one of the best in the world. His scientific results became classical and laid the foundation for such scientific areas as topological algebra, spaces of continuous functions, topological homogeneity. He wrote more than 330 works, more than fifty times A.V. Arhangelskii was an invited speaker at international conferences and symposiums. Monographs of A.V. Arhangel’skii “Topological function spaces”, “Cantor set theory”, “Finite-dimensional vector spaces”, “Topological groups and related structures” (joint with M.G. Tkachenko) and joint with V.I. Ponomarev textbook “Fundamentals of General Topology in Problems and Exercises” became reference books for many mathematicians and translated into foreign languages. He established in Russia an authoritative scientific school: among the students of A.V. Arhangelskii 37 candidates and doctors of science, among them more than 20 professors.

Topics include:
1. Set-Theoretic Topology
2. Mappings and Spaces
3. Topological groups
4. Topological function spaces

## Organizers

Lomonosov Moscow State University, Механико-математический факультет

#### Programme Committee:

V.A. Sadovnichy (chairman) – Academician, rector of Moscow Lomonosov State University S.P. Gul’ko – Head of the Department of Mathematical Analysis and Theory of Functions of Tomsk State University J. van Mill – professor University of Amsterdam (Nerthelands) M.G. Tkachenko – professor Universidad Autonoma Metropolitana (Mexico) V.V. Uspenskii – professor  Ohio University (USA) V.V. Filippov – professor Faculty of Mechanics and Mathematics of Moscow Lomonosov State University M.M. Choban – Academician AN Moldova,  Head of the Department of Algebra, Geometry and Topology of Tiraspol State University

#### Organizing Committee:

V.N. Chubarikov (co-chairman) – Acting Dean of the Faculty of Mechanics and Mathematics of Moscow Lomonosov State University Yu.V. Sadovnichy (co-chairman) – Head of the Department of General Topology and Geometry of Faculty of Mechanics and Mathematics of Moscow Lomonosov State University D.P. Baturov – associate professor of Orel State University A.N. Karpov – associate professor of Faculty of Mechanics and Mathematics of Moscow Lomonosov State University K.L. Kozlov – professor of Faculty of Mechanics and Mathematics of Moscow Lomonosov State University O.I. Pavlov – associate professor of RUDN University E.A. Reznichenko – associate professor of Faculty of Mechanics and Mathematics of Moscow Lomonosov State University O.V. Sipacheva – principal researcher of Faculty of Mechanics and Mathematics of Moscow Lomonosov State University A.N. Yakivchik – associate professor of Faculty of Mechanics and Mathematics of Moscow Lomonosov State University I.V. Yaschenko – principal of the Center for Pedagogical Excellence in the City of Moscow

## Cost of participation

The conference fee is 1000 roubles.

## Anthony Bonato: The new world of infinite random geometric graphs

Place: Fields Institute (Room 210)

Date: April 20, 2018 (13:30-15:00)

Speaker: Anthony Bonato

Title: The new world of infinite random geometric graphs

Abstract:

The \emph{infinite random} or \emph{Rado graph} $R$ has been of interest to graph theorists, probabilists, and logicians for the last half-century. The graph $R$ has many peculiar properties, such as its \emph{categoricity}: $R$ is the unique countable graph satisfying certain adjacency properties. Erd\H{o}s and R\'{e}nyi proved in 1963 that a countably infinite binomial random graph is isomorphic to $R$.

Random graph processes giving unique limits are, however, rare. Recent joint work with Jeannette Janssen proved the existence of a family of random geometric graphs with unique limits. These graphs arise in the normed space $\ell _{\infty }^{n}$, which consists of $\mathbb{R}^{n}$ equipped with the $L_{\infty }$-norm. Balister, Bollob\'{a}s, Gunderson, Leader, and Walters used tools from functional analysis to show that these unique limit graphs are deeply tied to the $L_{\infty }$-norm. Precisely, a random geometric graph on any normed, finite-dimensional space not isometric $\ell _{\infty}^{n}$ gives non-isomorphic limits with probability $1$.

With Janssen and Anthony Quas, we have discovered unique limits in infinite dimensional settings including sequences spaces and spaces of continuous functions. We survey these newly discovered infinite random geometric graphs and their properties.

## Marek Bienias: About universal structures and Fraisse theorem

Tuesday, April 24, 2018, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Marek Bienias (Łódź University of Technology)

Title: About universal structures and Fraisse theorem

Abstract:

For a given structure D of language L we can consider age of D, i.e. the family of all finitely generated L-substructures od D. It turns out that age has property (HP) and (JEP). Fraisse theorem let us revers the procedure: if K is nonempty countable family of finitely generated L-structures having properties (HP), (JEP) and (AP), then there exists exactly one (up to isomorphism) L-structure D (so called Fraisse limit) which is countable ultrahomogenous and has age K.
The aim of the talk is to define basic notions from Fraisse theory, proof the main theorem and show some alternative way of looking at the construction of Fraisse limit.

## Diana Carolina Montoya: On some ideals associated with independent families

Talk held by Diana Carolina Montoya (KGRC) at the KGRC research seminar on 2018-04-19.

Title: On some ideals associated with independent families

Abstract. The concept of independence was first introduced by Fichtenholz and Kantorovic to study the space of linear functionals on the unit interval. Since then, independent families have been an important object of study in the combinatorics of the real line. Particular interest has been given, for instance, to the study of their definability properties and to their possible sizes.

In this talk we focus on two ideals which are naturally associated with independent families: The first of them is characterized by a diagonalization property, which allows us to add a maximal independent family along a finite support iteration of some ccc posets. The second ideal originates in Shelah’s proof of the consistency of $\mathfrak i\lt \mathfrak u$ (here $\mathfrak i$ and $\mathfrak u$ are  the independence and ultrafilter numbers respectively). Additionally, we study the relationship  between these two ideals for an arbitrary independent family $A$, and define a class of maximal  independent families — which we call densely independent — for which the ideals mentioned above  coincide. Building upon the techniques of Shelah we (1) characterize Sacks indestructibility for  such families in terms of properties of its associated diagonalization ideal, and (2) devise a countably closed poset which adjoins a Sacks indestructible densely maximal independent family.

This is joint work with Vera Fischer.

## Petr Simon

Dear all,

I regret to inform you that Petr Simon passed away on Saturday April
14th. The funeral will take place on Friday April 20th at noon in Prague – Strasnice.

Best,
David

## Jonathan Verner: Ultrafilters and models of arithmetic

The seminar meets on Wednesday April 18th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Jonathan Verner — Ultrafilters and models of arithmetic

## Samuel Alfaro Tanuwijaya: Introduction to surreal numbers

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 18 April 2018, 17:00 hrs

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

Speaker: Samuel Alfaro Tanuwijaya

Title: Introduction to surreal numbers

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

In this talk, I will introduce the basic definitions of the surreal
numbers and their ordering given in the book by Harry Gonshor, and
their relations to the definitions given by Conway and Knuth. I will
then continue with the definitions operations on the numbers, such as
addition, multiplication, and division, and then prove that the
surreal numbers form a field. I will then establish that the surreal
numbers contain the real numbers and the ordinals.

## Appalachian Set Theory workshop: Dilip Raghavan, June 2, 2018

Appalachian set theory

# Dilip Raghavan : “Boolean ultrapowers and iterated forcing”

## Description

In joint work with Saharon Shelah, we develop a new method for proving consistency results on cardinal invariants, particularly results involving the invariant . This method can be used with a wide range of forcing notions, including arbitrary ccc posets. However the method always requires a supercompact cardinal κ in the ground model and produces forcing extensions in which the desired invariants sit above κ. Another feature of our method is that it generalizes to cardinal invariants above ω, and can be used to give uniform consistency proofs that work at any regular cardinal. It can also be used to treat situations where three cardinal invariants must be separated. In particular, our technique solves various long standing open problems about cardinal invariants at uncountable regular cardinals. All the results use Boolean ultrapowers, studied by Keisler and other model theorists in the 1960s. I will aim to give a fairly self contained introduction to this method and to some to its applications to the theory of cardinal invariants.

## Local information

The nearest airport is Pittsburgh International Airport. The Supershuttle shared van service is cheaper but slower than taking a taxi from the airport.

## Lodging

VERY IMPORTANT NOTE ABOUT LODGING: A block of rooms earmarked for attendees has been set aside at a local hotel (the Shadyside Inn). If we are covering your lodging expenses then we will need to make a reservation for you. Please don’t make your own reservation if we have promised you support, this will cause confusion and may make it impossible for us to reimburse you.

## Participant travel support

Funds provided by the National Science Foundation will be used to reimburse some participant transportation and lodging expenses. Priority will be given to students and faculty who do not hold federal research grants. Please request such funds as far in advance of the meeting as possible by sending the following information to the email address appalachiansettheory@gmail.com