archernikov - Network

There will be a Very Informal Gathering of Logicians (VIG 2025) at UCLA, Fri, Feb 7 to Sun, Feb 9, 2025. The 22nd in a series of biennial...

There will be a Very Informal Gathering of Logicians (VIG 2025) at UCLA, Fri, Feb 7 to Sun, Feb 9, 2025.
The 22nd in a series of biennial logic meetings at UCLA, this event honors Alexander Kechris on the occasion of his formal retirement from Caltech.

https://www.math.ucla.edu/~ineeman/Conf/VIG2025/

I'm giving a talk at the Harvard University Center of Mathematical Sciences and applications on Monday, on connections of mathematical...

I'm giving a talk at the Harvard University Center of Mathematical Sciences and applications on Monday, on connections of mathematical logic and higher VC-theory for learning in product spaces:
https://cmsa.fas.harvard.edu/event/colloquium-102124/

See some recommendations from me and my colleagues at the University of Maryland for your summer reading list. My recommendation is a...

See some recommendations from me and my colleagues at the University of Maryland for your summer reading list. My recommendation is a rollercoaster biography of a remarkable Polish logician and mathematician Alfred Tarski, "the man who defined truth"!

https://cmns.umd.edu/news-events/news/summer-reads-2024

In this paper, using quite different methods, we obtain a remarkable counterpart of the aforementioned classical theory for locally compact...

In this paper, using quite different methods, we obtain a remarkable counterpart of the aforementioned classical theory for locally compact topological groups, and classify idempotent generically stable measures in abelian groups as (unique) translation invariant measures on type-definable subgroups.
We also provide an explicit construction of a minimal left ideal in the convolution semigroup of measures for an arbitrary countable NIP group, from a minimal left ideal in the corresponding semigroup on types and a canonical measure constructed on its ideal subgroup. In order to achieve it, we in particular prove the revised Ellis group conjecture of Newelski for countable NIP groups! (Previously only known in the amenable case, by "Definably amenable NIP groups", Chernikov, Simon, J. Amer. Math. Soc. 2018, https://www.ams.org/journals/jams/2018-31-03/S0894-0347-2018-00896-3/)

Very excited about this new preprint, with Kyle Gannon and Krzysztof Krupinski!"Definable convolution and idempotent Keisler measures...

Very excited about this new preprint, with Kyle Gannon and Krzysztof Krupinski!

"Definable convolution and idempotent Keisler measures III. Generic stability, generic transitivity, and revised Newelski's conjecture"
https://arxiv.org/abs/2406.00912

Classical work by Wendel, Rudin, Cohen (before inventing forcing) and others classifies idempotent Borel measures on locally compact abelian groups, showing that they are precisely the Haar measures of compact subgroups.
We are interested in a counterpart of this phenomenon in the definable category. In the same way as e.g. algebraic or Lie groups are important in algebraic or differential geometry, the understanding of groups definable in a given first-order structure (or in certain classes of first-order structures) is important for model theory and its applications. The class of stable groups is at the core of model theory, and the corresponding theory was developed in the 1970s-1980s borrowing many ideas from the study of algebraic groups over algebraically closed fields. More recently, many of the ideas of stable group theory were extended to the class of NIP groups, which contains both stable groups and groups definable in o-minimal structures or over the p-adics. This led to multiple applications, e.g. a resolution of Pillay’s conjecture for compact o-minimal groups, or Hrushovski’s work on approximate subgroups. This brought to light the importance of the study of invariant measures on definable subsets of the group, as well as the methods of topological dynamics. In particular, deep connections with tame dynamical systems as studied by Glasner, Megrelishvili and others have emerged.

#Mathematics #ModelTheory #TopologicalDynamics

A new book by David Marker "An Invitation to Mathematical Logic" has recently been published in Springer's Graduate Texts in...

A new book by David Marker "An Invitation to Mathematical Logic" has recently been published in Springer's Graduate Texts in Mathematics series!

https://link.springer.com/book/10.1007/978-3-031-55368-4

Some of you may know his previous book "Model Theory : An Introduction", which served as a de facto standard intro to modern model theory for many years now (and was a start of my personal journey in model theory). This new book is intended as a text for a first graduate logic course. It grew out of Dave's lecture notes developed over many years teaching this material at the University of Illinois Chicago. A draft of the introduction and table of contents can be found here:
http://www.math.uic.edu/~marker/ml-web.pdf

I gave a short informal interview while visiting University of Münster last month:https://youtu.be/UJazzknGBqQ?si=wfvn7JEMhKSvTcyD@ramellus...

I gave a short informal interview while visiting University of Münster last month:

https://youtu.be/UJazzknGBqQ?si=wfvn7JEMhKSvTcyD

@ramellus and I discuss some history of mathematical logic and model theory, and one of the recent active directions connecting model theory and combinatorics, focusing around the question of recognizing algebraic or Lie groups among the algebraic varieties that have large intersections with finite grids of points. We also briefly discuss some future directions and open problems.

This conversation followed my more technical talk on the topic that you can see here:
https://youtu.be/njusBvm9MAk?si=QTY1dUrdQRpMZ8uj

The relevant paper and references in it appeared recently in Duke:
https://arxiv.org/abs/2104.02235

Accidentally, this was my peak math professor look - the longest beard I've ever had!

Check out also the other conversations in the series, Mihalis Dafermos from Princeton University, Jessica Fintzen from Bonn University, and more to come:
https://www.uni-muenster.de/MathematicsMuenster/news/mmconversations/index.shtml

Working on my fitness by practicing some very challenging superpositions.

Working on my fitness by practicing some very challenging superpositions.

A special issue of the new journal Model Theory is out! On the occasion of Ehud Hrushovski's Sixtieth Birthday, edited by Assaf Hasson,...

A special issue of the new journal Model Theory is out! On the occasion of Ehud Hrushovski's Sixtieth Birthday, edited by Assaf Hasson, H. Dugald Macpherson and Silvain Rideau-Kikuchi

https://msp.org/mt/2023/2-2/

"Géomètre expert" à Sisteron.

"Géomètre expert" à Sisteron.

Slides from my talk in Beijing today about recent joint work with @htowsner on a strong version of the regularity lemma for slice-wise...

Slides from my talk in Beijing today about recent joint work with @htowsner on a strong version of the regularity lemma for slice-wise stable hypergraphs.

https://www.math.ucla.edu/~chernikov/slides/Beijing2023.pdf

Yesterday all my troubles seemed so far away.

Yesterday all my troubles seemed so far away.

Congrats Dr. Derek Levinson!https://escholarship.org/uc/item/5gn7n86h

Congrats Dr. Derek Levinson!

https://escholarship.org/uc/item/5gn7n86h

Doing my part.

Doing my part.

Enjoyed my stay at Hilbert!

Enjoyed my stay at Hilbert!

Beijing #Logic Meeting in July 24-28, 2023!https://lcs.ios.ac.cn/blm/

Beijing #Logic Meeting in July 24-28, 2023!
https://lcs.ios.ac.cn/blm/

A workshop and a conference on #ModelTheory in Wroclaw, Poland this Fall! Model Theory Workshop: 15 - 18 September...

A workshop and a conference on #ModelTheory in Wroclaw, Poland this Fall!

Model Theory Workshop: 15 - 18 September 2023
https://math.uni.wroc.pl/~pkowa/registrationw23.html

Model Theory Conference: 19 - 23 September 2023
https://math.uni.wroc.pl/~pkowa/registrationc23.html

#ModelTheory Conference in Seoul, in commemoration of Byunghan Kim’s 60th birthday.Aug. 28-30, 2023The registration deadline is June 15,...

#ModelTheory Conference in Seoul, in commemoration of Byunghan Kim’s 60th birthday.

Aug. 28-30, 2023

The registration deadline is June 15, 2023.
This conference is ASL-sponsored, so students (who are ASL members) are eligible for ASL travel support. Partial travel expenses can also be provided to those who present a poster.

https://sites.google.com/yonsei.ac.kr/modeltheoryseoul2023/home?authuser=0

The video of my yesterday's talk at the #IAS on some uses of #ModelTheory in #Erdős #Geometry is now online. (Please ignore the...

The video of my yesterday's talk at the #IAS on some uses of #ModelTheory in #Erdős #Geometry is now online. (Please ignore the nonsense that I've said instead of the definition of modularity!)

https://youtu.be/w5ITepQZL8U

First time in #Atlanta! Speaking at the "#Logic, #Combinatorics, and Their Interactions" special session at the AMS Sectional...

First time in #Atlanta! Speaking at the "#Logic, #Combinatorics, and Their Interactions" special session at the AMS Sectional Meeting at Georgia Tech over the weekend.

abernshteyn3.math.gatech.edu/AMSLogicCombi/