Department of

# Mathematics

Seminar Calendar
for Model Theory and Descriptive Set Theory Seminar events the year of Saturday, November 9, 2019.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     October 2019          November 2019          December 2019
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5                   1  2    1  2  3  4  5  6  7
6  7  8  9 10 11 12    3  4  5  6  7  8  9    8  9 10 11 12 13 14
13 14 15 16 17 18 19   10 11 12 13 14 15 16   15 16 17 18 19 20 21
20 21 22 23 24 25 26   17 18 19 20 21 22 23   22 23 24 25 26 27 28
27 28 29 30 31         24 25 26 27 28 29 30   29 30 31



Friday, February 8, 2019

4:00 pm in 345 Altgeld Hall,Friday, February 8, 2019

#### "The complexity of topological group isomorphism" by A. Kechris, A. Nies, and K. Tent (Part 1)

###### Anush Tserunyan (UIUC)

Abstract: This will be the introductory talk of the series on the paper in the title [arXiv link], which deals with the classification of some natural classes of non-Archimedean groups (= closed subgroups of S) up to topological group isomorphism. It gives a general criterion for a class of non-Archimedean groups to show that the topological group isomorphism on it is Borel-classifiable by countable structures. This criterion is satisfied by the classes of profinite groups, locally compact non-Archimedean groups, and oligomorphic groups.

Friday, February 15, 2019

3:00 pm in 341 Altgeld Hall ,Friday, February 15, 2019

#### Note the time and room change!"The complexity of topological group isomorphism" by A. Kechris, A. Nies, and K. Tent (Part 2)

###### Jenna Zomback (UIUC)

Abstract: This will be the second talk of the series on the paper in the title [arXiv link], which deals with the classification of some natural classes of non-Archimedean groups (= closed subgroups of S) up to topological group isomorphism. It gives a general criterion for a class of non-Archimedean groups to show that the topological group isomorphism on it is Borel-classifiable by countable structures. This criterion is satisfied by the classes of profinite groups, locally compact non-Archimedean groups, and oligomorphic groups. In this talk, we will fill in some proofs left out last time and prove this general criterion.

Friday, February 22, 2019

4:00 pm in 345 Altgeld Hall ,Friday, February 22, 2019

#### Cancelled

Friday, March 1, 2019

4:00 pm in 345 Altgeld Hall ,Friday, March 1, 2019

#### "The complexity of topological group isomorphism" by A. Kechris, A. Nies, and K. Tent (Part 3)

###### Mary Angelica Gramcko-Tursi (UIUC)

Abstract: This will be the third talk of the series on the paper in the title [arXiv link], which deals with the classification of some natural classes of non-Archimedean groups (= closed subgroups of S) up to topological group isomorphism. It gives a general criterion for a class of non-Archimedean groups to show that the topological group isomorphism on it is Borel-classifiable by countable structures. This criterion is satisfied by the classes of profinite groups, locally compact non-Archimedean groups, and oligomorphic groups. In this talk, we will show that one or two of the aforementioned classes satisfy this criterion.

Friday, March 8, 2019

4:00 pm in 345 Altgeld Hall ,Friday, March 8, 2019

#### Organizational meeting

Friday, March 15, 2019

4:00 pm in 345 Altgeld Hall ,Friday, March 15, 2019

#### The theory of addition with predicates for the powers of 2 and 3

###### Christian Schulz (UIUC Math)

Abstract: This talk concerns the intricate boundary between decidable and undecidable of expansions of Presburger artithmetic, i.e., the structure $(\mathbb{N}, +)$. For a natural number $p \ge 2$, let $p^{\mathbb{N}}$ denote the set of powers of $p$, and let $V_p$ be a predicate that allows us to access the full base-$p$ expansion of a natural number. It is known that the expansion $(\mathbb{N}, +, V_p)$ of Presburger arithmetic retains decidability, but $(\mathbb{N}, +, V_p, q^{\mathbb{N}})$, for $q$ multiplicatively independent from $p$, has an undecidable theory. In this talk, I present a proof that the reduct $(\mathbb{N}, +, p^{\mathbb{N}}, q^{\mathbb{N}})$ also has an undecidable theory, specifically in the case $p = 2$, $q = 3$. I conclude with a note on how the proof extends to other structures, as well as some discussion of directions for further research.

Friday, April 5, 2019

4:00 pm in 345 Altgeld Hall ,Friday, April 5, 2019

#### Generic derivations on o-minimal structures

###### Elliot Kaplan (UIUC Math)

Abstract: We study derivations $\delta$ on o-minimal fields $K$. We introduce the notion of a $T$-derivation, which is a derivation which cooperates with the 0-definable $\mathcal{C}^1$-functions on $K$. For example, if $K$ is an elementarily equivalent to the real exponential field, we require that $\delta \exp(a) = \exp(a)\delta a$ for all $a \in K$. Let $T$ be the theory of $K$ in an appropriate language $L$ and let $T^\delta$ be the $L\cup \{\delta\}$ theory stating that $\delta$ is a $T$-derivation. We show that if $T$ has quantifier elimination, then $T^\delta$ has a model completion $T^\delta_G$. The derivation in models $K$ of $T^\delta_G$ behaves "generically," it is wildly discontinuous and its kernel is a dense elementary $L$-substructure of $K$. If $T$ is the theory of real closed ordered fields, then $T^\delta_G$ is the theory of closed ordered differential fields (CODF) as introduced by Michael Singer. We are able to recover many of the known facts about CODF in our setting. Among other things, we show that $T^\delta_G$ has $T$ as its open core and that $T^\delta_G$ is distal. This is joint work with Antongiulio Fornasiero.

Friday, April 19, 2019

4:00 pm in 345 Altgeld Hall ,Friday, April 19, 2019

#### Cancelled

###### (UIUC Math)

Friday, September 6, 2019

4:00 pm in 345 Altgeld Hall,Friday, September 6, 2019

#### "On the nonexistence of Følner sets" by Isaac Goldbring

###### Elliot Kaplan (UIUC Math)

Abstract: This will be the first (and possibly only) talk on the preprint "On the nonexistence of Følner sets" by Isaac Goldbring (https://arxiv.org/abs/1901.02445). I will introduce all of the necessary model-theoretic and group-theoretic background. Time permitting, I may get to the proof of the main result.

Friday, September 20, 2019

4:00 pm in 345 Altgeld Hall,Friday, September 20, 2019

#### A Logician's Introduction to the Problem of P vs. NP

###### Alexi Block Gorman (UIUC Math)

Abstract: Central to much of computer science, and some areas of mathematics, are questions about various problems' computability and complexity (whether the problem can be solved "algorithmically," and how "hard" it is to do so). In this talk, I will first give an overview of the complexity hierarchy for machines (from finite automata to Turing machines) and the mathematical properties of the space of languages that we associate with them. Next, I will discuss the relationship of deterministic and non-deterministic machines, which will allow us to segue from questions of computability to that of complexity. Finally, I will give a precise formulation of the problem of P vs. NP, and try to illustrate why the problem remains rather elusive. This talk does not require any background in logic or computer science, and should be accessible to all graduate students.

Friday, September 27, 2019

4:00 pm in 345 Altgeld Hall,Friday, September 27, 2019

#### O-minimal complex analysis according to Peterzil–Starchenko (Part 1)

###### Lou van den Dries (UIUC)

Abstract: This is the first of two survey talks on the subject of the title. Neer (and others?) will follow up with a more detailed treatment in later talks. O-minimal complex analysis is one way that ideas from o-minimality have been used in recent work in arithmetic algebraic geometry (Pila, Zannier, Tsimerman, Klingler,…), the other one being the Pila–Wilkie theorem. The two topics relate because important objects like the family of Weierstrass p-functions turn out to be "o-minimal".

Friday, October 4, 2019

4:00 pm in 345 Altgeld Hall,Friday, October 4, 2019

#### O-minimal complex analysis according to Peterzil–Starchenko (Part 2)

###### Lou van den Dries (UIUC)

Abstract: This is the first of two survey talks on the subject of the title. Neer (and others?) will follow up with a more detailed treatment in later talks. O-minimal complex analysis is one way that ideas from o-minimality have been used in recent work in arithmetic algebraic geometry (Pila, Zannier, Tsimerman, Klingler,…), the other one being the Pila–Wilkie theorem. The two topics relate because important objects like the family of Weierstrass p-functions turn out to be "o-minimal".

Friday, October 11, 2019

4:00 pm in 345 Altgeld Hall,Friday, October 11, 2019

#### "Complex-like" analysis in o-minimal structures (Part 3)

###### Neer Bhardwaj (UIUC)

Abstract: Analogues of many of the basic results in complex analysis can be established over an arbitrary algebraically closed field $K$ of characteristic zero, in the context of an o-minimal expansion of a real closed field $R$, with $K=R[i]$. I will show in particular how one can define winding numbers, and how differentiability begets infinite differentiability in this setting. This expository talk follows the survey given by Lou in the last two weeks and will be based mostly on: "Expansions of algebraically closed fields in o-minimal structures" by Starchenko–Peterzil (https://link.springer.com/article/10.1007/PL00001405)

Friday, November 1, 2019

4:00 pm in 345 Altgeld Hall,Friday, November 1, 2019

#### O-minimal complex analysis (Part 4)

###### Elliot Kaplan (UIUC)

Abstract: I will continue discussing Peterzil and Starchenko's treatment of definable functions on the algebraic closure of an o-minimal field.

Friday, November 8, 2019

4:00 pm in 345 Altgeld Hall,Friday, November 8, 2019

#### O-minimal complex analysis (Part 5)

###### Elliot Kaplan (UIUC)

Abstract: I will continue discussing Peterzil and Starchenko's treatment of definable functions on the algebraic closure of an o-minimal field.