## Ian Herbert: Weak Lowness Notions and Weak Reducibilities

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 12 March 2014, 17:00 hrs

Room: S17#04-05, Department of Mathematics, NUS

Speaker: Ian Herbert

Title: Weak Lowness Notions and Weak Reducibilities

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

Abstract: The prefix-free Kolmogorov complexity of a finite binary string
is the length of the shortest description of the string, according to some
universal decoding machine. This gives rise to some `standard’ lowness
notions for reals: A is K-trivial if its initial segments have the
lowest possible complexity and A is low for K if using A as an oracle
does not decrease the complexity of strings by more than a constant
factor. We discuss various ways of weakening these notions and the
relations among these weakenings and between them and standard
notions. We also discuss how these notions behave under reducibilities
that are based on Kolmogorov complexity and are weaker than Turing
reducibility.

## Ramsey theory conference, May 24 – 28, 2014

Ramsey theory conference, University of Denver. May 24–28, 2014

The aim of this conference is to bring together students and researchers from around the world in the field of Ramsey Theory. The focus is on structural and infinitary Ramsey theory and applications to other fields of mathematics, including Banach spaces, Boolean algebras, Set Theory, and Topological Dynamics. The conference will consist of a large number of plenary talks and contributed talks of 25 minutes. The official language of the conference is English.
Invited speakers (confirmed so far):

· Antonio Aviles (University of Murcia, Spain)

· Dana Bartosova (University of Sao Paulo, Brazil)

· Ari Brodsky (University of Toronto, Canada)

· Carlos Di Prisco (Instituto Venezolano de Investigaciones Científicas, Venezuela)

· Neil Hindman (Howard University, USA)

· Michael Hrusack (Universidad Nacional Autónoma de México, Mexico)

. Alexander Kechris (Cal Tech, USA)

· Jean Larson (University of Florida at Gainsville, USA)

· Brice Mbombo (University of Sao Paulo, Brazil)

· Diana Ojeda (Cornell University, USA)

· Claribeth Pina, (University of Paris 7, France)

· Slawomir Solecki (University of Illinois at Urbana-Champaign, USA)

· Stevo Todorcevic (University of Toronto, Canada/ University of Paris 7, France)

· Timothy Trujillo, (University of Denver, USA)

· Anush Tserunyan (University of Illinois at Urbana-Campaign, USA) Continue reading

## Juris Steprans: Non-trivial automorphisms of $P(\omega_1)/fin$

7 March 2014, 13:30–15:00
Fields institute, Room 210

Speaker:  Juris Steprans

Title:  Non-trivial automorphisms of $P(\omega_1)/fin$

Abstract:
Just as in the case of automorphisms of $P(\omega)/fin$, an automorphism of $P(\omega_1)/fin$ will be called trivial if it is induced by a bijection between cofinite subsets of $\omega_1$. Since a non-trivial automorphism of $P(\omega)/fin$ can easily be extended to a non-trivial automorphism of $P(\omega_1)/fin$ there is little interest examining the existence of non-trivial automorphisms of $P(\omega_1)/fin$ without further restrictions. So, an automorphism of $P(\omega_1)/fin$ will be called really non-trivial if it is non-trivial, yet its restriction to any subalgebra of the form $P(X)/fin$ is trivial when $X$ is countable.
It will be shown to be consistent with set theory that there is a really non-trivial automorphism of $P(\omega_1)/fin$. This is joint work with Assaf Rinot.

## 10/Mar/2014: Grigor Sargsyan and Scott Cramer

All talks are in Hill

DST Seminar at 3:20 Room 525

Monday 03/10 — Grigor Sargsyan (Rutgers)
Title: Stability and Morley rank IV

Logic Seminar at 5:00 Room 705

Monday 03/10 — Scott Cramer (Rutgers)
Title: Inverse Limit Reflection I

## Chris Lambie-Hanson: Jónsson cardinals, partition relations, and stationary reflection, Part III

Speaker:  Chris Lambie-Hanson

Title: Jónsson cardinals, partition relations, and stationary reflection, Part III

Abstract: I will present a proof that, relative to large cardinal assumptions, it is consistent that there is a singular cardinal
mu such that every stationary subset of mu^+ reflects but that there is a stationary subset of mu^+ that does not reflect at
ordinals of arbitrarily high cofinality. This answers a question of Eisworth motivated by the study of Jónsson cardinals and
square-bracket partition relations and is joint work with James Cummings.

## Rupert Hoelzl: Randomness in the Weihrauch degrees

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 05 March 2014, 17:00 hrs

Room: S17#04-05, Department of Mathematics, NUS

Speaker: Rupert Hoelzl

Title: Randomness in the Weihrauch degrees

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

Abstract: The Weihrauch degrees are a degree structure that can be used to
classify how complex it is to find solutions to certain mathematical
tasks, that typically arise from classical mathematical theorems, for
example in analysis. We will give an overview over recent work about
interactions between these degrees and the field of algorithmic
randomness. In particular we will discuss where two different models of
randomized computation are located in this lattice: computation with
access to a Martin-Löf random oracles and computation with a Las Vegas
algorithm. We will see that these two models can be separated in the
Weihrauch degree, which is in contrast to results in the related field
of reverse maths, where they are known to coincide. After briefly
discussing some other results relating the two subjects mentioned above,
we present some open questions.

## Itay Kaplan: Strict non-forking in resilient theories

Mathematical Logic Seminar (HUJI)

The speaker on March 5 is Itay Kaplan
Title: Strict non-forking in resilient theories
Abstract:
Strict non-forking is a forking notion defined by Shelah for NIP theories and proved very useful in analysing dividing in NIP and NTP2 theories. In joint work with Alex Usvyatsov, we proved symmetry of this notion in NIP. Recently we generalized this to a more general setting, that of resilient theories.
Resilient theories were defined by Chernikov and Ben-Yaacov as a class of theories containing both NIP and simple theories and contained in NTP2 theories.
I will give all the definitions and try to prove the theorem.

The
logic seminar  takes place on Wednesdays at 16:00, in room 209T

## Postdoc Position in Set Theory in Torino (Italy), 2014-2015

16 MONTHS POSTDOC POSITION IN SET THEORY IN TORINO (ITALY)

There is an opening for a 16 months post doc position in set theory in the department of mathematics of Torino university starting may 1st 2014 and finishing august 31st 2015. Applicants are required to be less than 35 and must have earned their Ph.D. title. It is also required to the applicants to have at least one publication in a peer reviewed journal in the last three years. The net salary is slightly more than 1400 euros per month which allow for a reasonable living in Torino, extra money for research and travel can be given. The post doc will join the logic group of the department which consists of Matteo Viale, Alessandro Andretta, Riccardo Camerlo (polytechnical university), Daisuke Ikegami (set theory), Domenico Zambella (model theory). In the fall Daisuke Ikegami will leave and Luca Motto Ros (currently in freiburg) will most likely join the group. The selection of applicants will be based on an evaluation of the CV, of the publication records, and of their interests of research which must be in set theory. It is possible to file online the applications creating an account on the italian ministry of education website. If you intend to apply write to matteo.viale@unito.it in order to get detailed information on the filing procedure.
Applicants can deposit their online registration forms since today up to the 19th of march 2014.
Those passing a first selection will be admitted to a (skype) interview which will take place most likely in the end of march-beginning of April. The position starts at the earliest on may 1st 2014, but the starting (not the ending period) can eventually be delayed.
Due to a very restrictive law on immigration, non EU-applicant should consider that the constraint on the expiration of the grant and the time required to get their working visa may shorten significantly the length of the period in which they can use the grant.

## Daniel Soukup: Davies-trees in infinite combinatorics

28 February 2014, 13:30–15:00
Fields institute, Room 210

Speaker:  Daniel Soukup

Title:  Davies-trees in infinite combinatorics

Abstract:

The aim of this talk is to introduce Davies-trees and present new applications to combinatorics. Davies-trees are special sequences of countable elementary submodels which played important roles in generalizing arguments using CH to pure ZFC proofs. My goal is to present two unrelated but fascinating results due to P. Komjáth: we prove that the plane is the union of n+2 “clouds” provided that the continuum is at most $\aleph_n$ and that every uncountably chromatic graph contains k-connected uncountably chromatic subgraphs for each finite k. We hopefully have time to review the most important open problems around the second theorem.

## Chris Lambie-Hanson: Jónsson cardinals, partition relations, and stationary reflection, Part II

CMU math logic seminar Tue Feb 25

Speaker:  Chris Lambie-Hanson

Title: Jónsson cardinals, partition relations, and stationary reflection, Part II

Abstract: I will present a proof that, relative to large cardinal assumptions, it is consistent that there is a singular cardinal
mu such that every stationary subset of mu^+ reflects but that there is a stationary subset of mu^+ that does not reflect at
ordinals of arbitrarily high cofinality. This answers a question of Eisworth motivated by the study of Jónsson cardinals and
square-bracket partition relations and is joint work with James Cummings.