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)
To Be Announced

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)
To Be Announced

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)
TBA

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)
To Be Announced