Seminar Calendar
for Logic Seminar events the next 12 months of Sunday, January 1, 2017.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, January 24, 2017

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, January 24, 2017
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Submitted by anush.
Evgeny Gordon (Eastern Illinois Math)
Will the Nonstandard Analysis become the Analysis of Future?
Abstract: In 1973 Abraham Robinson gave a talk about the nonstandard analysis (NSA) at the Institute for Advanced Study. After his talk Kurt G\"odel made a comment, in which he predicted that "...there are good reasons to believe that Non-Standard Analysis in some version or other will be the analysis of the future". One has to admit that during the fifty years since this prediction, it did not come true. One of the reasons is that the most part of researchers in NSA considered it as a tool of obtaining new results in standard mathematics, instead of consider it as a more appropriate language, in which the "book of nature is written". Nowadays, the investigation of DE's that simulate processes in science and economy are based on computer (discrete) simulations of these DE's.
  In this talk I will try to justify the point of view that the language of NSA is more appropriate for investigation of the interaction between continuous models and their discrete simulations (or maybe vise versa - between discrete models and their continuous simulation, according to a popular among applied mathematicians point of view). The reason is that not well defined properties ("very big", "very small", "far enough of the boundaries of computer memory", etc.) can be introduced in the language of NSA on the level of rigor of Cantor's Set Theory. I will discuss some NSA theorems in algebra, calculus, ergodic theorem and quantum mechanics) concerning this problem that have intuitively clear sense and agree with computer experiments, while their formulation in the language of standard mathematics looks irrelevant and sometimes even unreadable.

Tuesday, January 31, 2017

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, January 31, 2017
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Submitted by anush.
Victoria Noquez (UIC Math)
Uncountable Categoricity in Continuous Logic
Abstract: In recent years, some progress has been made towards understanding uncountable categoricity in the continuous setting, particularly in the context of classes of Banach spaces. Currently, it is unknown if the Baldwin-Lachlan characterization of uncountable categoricity holds in continuous logic. Namely, is it the case a continuous theory T is $\kappa$-categorical for some uncountable cardinal $\kappa$ if and only if T is $\omega$-stable and has no Vaughtian pairs?
 In order to address this question, we provide the necessary continuous characterization of Vaughtian pairs, and in the process, prove Vaught's two-cardinal theorem, as well as a partial converse of the theorem in the continuous setting. This allows us to prove the forward direction of the Baldwin-Lachlan characterization.
 Trying to prove the reverse direction leads us to an attempt to characterize strong minimality in continuous logic. We propose a notion of strong minimality, and show that it has many of the properties of its classical analogue. Unfortunately, we see that this does not provide the machinery required to show that $\omega$-stability and the absence of Vaughtian pairs are sufficient conditions for uncountable categoricity. We provide some examples towards understanding this failure.

Tuesday, February 7, 2017

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, February 7, 2017
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Submitted by anush.
Canceled

Tuesday, February 21, 2017

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, February 21, 2017
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Submitted by anush.
Erik Walsberg (UIUC Math)
"Strong theories of ordered abelian groups" by A. Dolich and J. Goodrick (2nd talk)

Tuesday, February 28, 2017

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, February 28, 2017
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Submitted by erikw.
Robert Kaufman (UIUC)
Complexity in Dual Banach Spaces
Abstract: X is a Banach space, X* is its dual space, composed of bounded linear functionals on X. The norm of a functional in X* is its supremum over the closed unit ball in X. NA is the set of functionals whose norm is attained there. S (for "sharp") is the set of functionals whose norm is attained at precisely one point in the closed ball. To obtain interesting conclusions about the complexity of these sets, the space X is re-normed. (This is not as scary as it sounds.)

Thursday, March 2, 2017

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Thursday, March 2, 2017
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Submitted by ssolecki.
Natasha Dobrinen (University of Denver)
Henson's universal triangle-free graphs have finite big Ramsey degrees
Abstract: A triangle-free graph on countably many vertices is universal triangle-free if every countable triangle-free graph embeds into it. Universal triangle-free graphs were constructed by Henson in 1971, which we will denote as $\mathcal{H}_3$. Being an analogue of the random graph, its Ramsey properties are of interest. Henson proved that for any partition of the vertices in $\mathcal{H}_3$ into two colors, there is either a copy of $\mathcal{H}_3$ in one color (furthermore, only leaving out finitely many vertices in the first color), or else the other color contains all finite triangle-free graphs. In 1986, Komj\'{a}th and R\"{o}dl proved that the vertices in $\mathcal{H}_3$ have the Ramsey property: For any partition of the vertices into two colors, one of the colors contains a copy of $\mathcal{H}_3$. In 1998, Sauer showed that there is a partition of the edges in $\mathcal{H}_3$ into two colors such that every subcopy of $\mathcal{H}_3$ has edges with both colors. He also showed that for any coloring of the edges into finitely many colors, there is a subcopy of $\mathcal{H}_3$ in which all edges have at most two colors. Thus, we say that the big Ramsey degree for edges in $\mathcal{H}_3$ is two. It remained open whether all finite triangle-free graphs have finite big Ramsey degrees; that is, whether for each finite triangle-free graph G there is an integer n such that for any finitary coloring of all copies of G, there is a subcopy of $\mathcal{H}_3$ in which all copies of G take on no more than n colors. We prove that indeed this is the case.

Tuesday, March 7, 2017

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, March 7, 2017
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Submitted by anush.
Henry Towsner (UPenn Math)
Relatively Random First-Order Structures
Abstract: The Aldous–Hoover Theorem gives a characterization of those random processes which generate "exchangeable" first-order structures. A random first-order structure on the natural numbers is exchangeable if, after any permutation of the natural numbers, it has the same distribution. The original proof of the full Aldous–Hoover Theorem used ultraproducts, and the topic remains intimately tied to the way probability measures behave in ultraproducts.
  For some purposes, full exchangeability is too strong. We investigate "relative exchangeability", where we only require that the distribution be preserved by automorphisms of a fixed first-order structure $M$. A full Aldous–Hoover theorem is not always possible in this setting, and how much we recover turns out to depend on the amalgamation properties of $M$.

Tuesday, March 14, 2017

Logic Seminar
1:00 pm   in Altgeld Hall,  Tuesday, March 14, 2017
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Submitted by erikw.
James Freitag (UIC Math)
Model theory and Painleve equations
Abstract: We will discuss how to use model theory to prove some transcendence results for solutions of Painleve equations.

Thursday, March 16, 2017

Logic Seminar
1:00 pm   in 243 Altgeld Hall,  Thursday, March 16, 2017
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Submitted by phierony.
Sergei Starchenko (Notre Dame)
On Grothendieck's proof of the Fundamental Theorem of Stability Theory
Abstract: In the paper "Model theoretic stability and definability of types, after A. Grothendieck" (2014) Itai Ben Yaacov observed that the Fundamental Theorem of Stability Theory (also known as the Definability of Types Theorem) follows from Grothendieck's paper "Critères de compacité dans les espaces fonctionnels généraux" (1952) on what can be called "double limits property". In this talk we discuss this connection and provide an elementary proof of a version of Grothendieck's theorem equivalent to the Fundamental Theorem of Stability Theory.

Tuesday, March 28, 2017

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, March 28, 2017
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Submitted by anush.
Dima Sinapova (UIC Math)
Simultaneous stationary reflection and failure of SCH
Abstract: We will show that it is consistent to have finite simultaneous stationary reflection at $\kappa^+$ with not SCH at $\kappa$. This extends a result of Assaf Sharon. We will also present an abstract approach of iterating Prikry type forcing and use it to bring our construction down to $\aleph_\omega$. This is joint work with Assaf Rinot.

Tuesday, April 4, 2017

Logic Seminar
1:00 pm   in UIC SEO 636,  Tuesday, April 4, 2017
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Submitted by phierony.
MidWest Model Theory Day at UIC
Abstract: see http://homepages.math.uic.edu/~freitag/MWMT11

Tuesday, April 25, 2017

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, April 25, 2017
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Submitted by erikw.
Nigel Pynn-Coates (UIUC)
Differential-henselian extensions
Abstract: The general motivating question is: What aspects of valuation theory can be adapted to the setting of valued differential fields, and under what assumptions? In valuation theory, henselian fields play an important role. I will concentrate on differential-henselian fields, introduced by Scanlon and developed in a more general setting by Aschenbrenner, van den Dries, and van der Hoeven. What do we know about uniqueness of differential-henselian extensions? Do differential-henselizations exist? After reviewing what is known, I will discuss my ongoing work towards answering these questions, and sketch a proof of the answers when the value group has finite archimedean rank. This talk is part of my preliminary examination.

Tuesday, August 29, 2017

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, August 29, 2017
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Submitted by anush.
Filippo Calderoni (University of Torino)
TBA

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, August 29, 2017
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Submitted by anush.
Filippo Calderoni (University of Torino)
TBA

Tuesday, September 5, 2017

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, September 5, 2017
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Submitted by anush.
Arman Darbinyan (Vanderbilt Math)
To Be Announced

Tuesday, September 12, 2017

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, September 12, 2017
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Submitted by anush.
Ronnie Chen (Caltech Math)
To Be Announced