Seminar Calendar
for Model Theory events the next 12 months of Saturday, August 1, 2009.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery. 
      July 2009             August 2009           September 2009   
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           1  2  3  4                      1          1  2  3  4  5
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                        30 31

Friday, August 28, 2009

Model Theory and Descriptive Set Theory
4:00 pm   in 345 Altgeld Hall,  Friday, August 28, 2009
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Submitted by w-henson.
van den Dries / Henson / Solecki (UIUC Math)
Sums and Products -- organizational meeting
Abstract: This semester we will focus our Friday logic seminars on a new development of general mathematical interest, involving descriptive set theory, combinatorics, number theory, and model theory. At this organizational meeting, a plan for the semester will be worked out. The first paper we'll read is "Borel subrings of the reals" by G.A. Edgar and Chris Miller. A main result of this paper is that if E is a proper subring of the field of real numbers that is also a Borel set, then the Hausdorff dimension of E is 0. Indeed, they show that for all n, the set E^n has Hausdorff dimension 0 as a subset of R^n. Further work to which our seminar will aim involves papers by Jean Bourgain, Terry Tao, and others, and especially a preprint by Udi Hrushovski. All interested people are warmly invited to participate.

Friday, September 4, 2009

Model Theory and Descriptive Set Theory
4:00 pm   in 345 Altgeld Hall,  Friday, September 4, 2009
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Submitted by w-henson.
Kostya Slutskyy (UIUC Math)
Sums and Products, I
Abstract: This talk will cover material from "Borel subrings of the reals" by G.A. Edgar and Chris Miller. A main result of this paper is that if E is a proper subring of the field of real numbers that is also a Borel set, then the Hausdorff dimension of E is 0. All interested people are warmly invited to participate.

Friday, September 11, 2009

Model Theory and Descriptive Set Theory
4:00 pm   in 345 Altgeld Hall,  Friday, September 11, 2009
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Submitted by w-henson.
Aleksandra Kwiatkowska (UIUC Math)
Sums and Products, II
Abstract: This is the first of three talks in this seminar about the paper "The sum-product phenomenon in arbitrary rings" by Terence Tao. (A preprint available from the arXiv.) A very rough statement of this phenomenon is: "if A is a finite non-empty subset of a suitable ring with A+A and AA both having size comparable to A, then A should be 'very close' to a ring (or a dilate of a ring) of size comparable to A."

Friday, September 18, 2009

Model Theory and Descriptive Set Theory
4:00 pm   in 345 Altgeld Hall,  Friday, September 18, 2009
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Submitted by w-henson.
C. Ward Henson (UIUC Math)
Sums and Products, III
Abstract: This is the second of three talks in this seminar about the paper "The sum-product phenomenon in arbitrary rings" by Terence Tao. (A preprint available from the arXiv.) A very rough statement of this phenomenon is: "if A is a finite non-empty subset of a suitable ring with A+A and AA both having size comparable to A, then A should be 'very close' to a ring (or a dilate of a ring) of size comparable to A."

Friday, September 25, 2009

Model Theory and Descriptive Set Theory
4:00 pm   in 345 Altgeld Hall,  Friday, September 25, 2009
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Submitted by w-henson.
Lou van den Dries (UIUC Math)
Sums and Products, IV
Abstract: This is the last of three talks in this seminar about the paper "The sum-product phenomenon in arbitrary rings" by Terence Tao. (A preprint available from the arXiv.) A very rough statement of this phenomenon is: "if A is a finite non-empty subset of a suitable ring with A+A and AA both having size comparable to A, then A should be 'very close' to a ring (or a dilate of a ring) of size comparable to A."

Friday, October 2, 2009

Model Theory and Descriptive Set Theory
4:00 pm   in 345 Altgeld Hall,  Friday, October 2, 2009
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Submitted by w-henson.
Shichang Song (UIUC Math)
Sums and Products, V
Abstract: This week we'll start looking at Udi Hrushovski's paper "Stable group theory and approximate subgroups". This first talk will be introductory, with discussion of some consequences of the main theorem of the paper. In the arXiv, this is paper 0909.2190v2 [math.LO]

Friday, October 9, 2009

Model Theory and Descriptive Set Theory
4:00 pm   in 345 Altgeld Hall,  Friday, October 9, 2009
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Submitted by w-henson.
Shichang Song (UIUC Math)
Sums and Products, VI
Abstract: This week we'll continue looking at Udi Hrushovski's paper "Stable group theory and approximate subgroups". This talk will again be introductory, with discussion of some consequences of the main theorem of the paper. In the arXiv, this is paper 0909.2190v2 [math.LO]

Friday, October 16, 2009

Model Theory and Descriptive Set Theory
4:00 pm   in 345 Altgeld Hall,  Friday, October 16, 2009
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Submitted by w-henson.
C. Ward Henson (UIUC Math)
Sums and Products, VII
Abstract: This week we'll start looking at section 2 in Udi Hrushovski's paper "Stable group theory and approximate subgroups". In the arXiv, this is paper 0909.2190v2 [math.LO]

Friday, October 23, 2009

Model Theory and Descriptive Set Theory
4:00 pm   in 345 Altgeld Hall,  Friday, October 23, 2009
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Submitted by w-henson.
C. Ward Henson (UIUC Math)
Sums and Products, VIII
Abstract: This week we'll continue looking at section 2 in Udi Hrushovski's paper "Stable group theory and approximate subgroups". In the arXiv, this is paper 0909.2190v2 [math.LO]

Friday, October 30, 2009

Model Theory and Descriptive Set Theory
4:00 pm   in 345 Altgeld Hall,  Friday, October 30, 2009
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Submitted by w-henson.
Lou van den Dries (UIUC Math)
Sums and Products, IX
Abstract: This week we'll continue looking at section 2 in Udi Hrushovski's paper "Stable group theory and approximate subgroups". In the arXiv, this is paper 0909.2190v2 [math.LO]

Friday, November 6, 2009

Model Theory and Descriptive Set Theory
4:00 pm   in 345 Altgeld Hall,  Friday, November 6, 2009
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Submitted by w-henson.
Lou van den Dries (UIUC Math)
Sums and Products, X
Abstract: This week we'll continue looking at section 2 in Udi Hrushovski's paper "Stable group theory and approximate subgroups". In the arXiv, this is paper 0909.2190v2 [math.LO]

Friday, November 13, 2009

Model Theory and Descriptive Set Theory
4:00 pm   in 345 Altgeld Hall,  Friday, November 13, 2009
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Submitted by w-henson.
Lou van den Dries (UIUC Math)
Sums and Products, XI
Abstract: This week we'll begin looking at section 3 in Udi Hrushovski's paper "Stable group theory and approximate subgroups", with a focus on understanding the statement of the main theorem (Theorem 3.4). In the arXiv, this is paper 0909.2190v2 [math.LO]

Friday, November 20, 2009

Model Theory and Descriptive Set Theory
4:00 pm   in 345 Altgeld Hall,  Friday, November 20, 2009
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Submitted by w-henson.
Lou van den Dries (UIUC Math)
Sums and Products, XII
Abstract: This week we'll continue looking at section 3 in Udi Hrushovski's paper "Stable group theory and approximate subgroups", with a focus on understanding the statement of the main theorem (Theorem 3.4) and proving some of its consequences. In the arXiv, this is paper 0909.2190v2 [math.LO]

Friday, January 29, 2010

Model Theory and Descriptive Set Theory
4:00 pm   in 345 Altgeld Hall,  Friday, January 29, 2010
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Submitted by w-henson.
C.W. Henson and S. Solecki (UIUC Math)
organizational meeting
Abstract: Discussion of topics to be taken up this semester in this working seminar. Roughly the first half of the semester will be devoted to the model theoretic and descriptive set theoretic properties of Gurarii's universal, homogeneous separable Banach space. We will construct it from scratch and prove its uniqueness (the model theory) and study the action of its automorphism group.

Friday, February 5, 2010

Model Theory and Descriptive Set Theory
4:00 pm   in 345 Altgeld Hall,  Friday, February 5, 2010
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Submitted by w-henson.
C.Ward Henson (UIUC Math)
Gurarii's Banach space, part 1
Abstract: In this seminar, the first half of the semester will be devoted to the model theoretic and descriptive set theoretic properties of Gurarii's universal, homogeneous separable Banach space. We will construct it from scratch and prove its uniqueness (the model theory) and study the action of its automorphism group. Today we'll discuss the project in outline and then start looking at some amalgamation emmas for Banach spaces that provide tools for what comes later.

Friday, February 12, 2010

Model Theory and Descriptive Set Theory
4:00 pm   in 345 Altgeld Hall,  Friday, February 12, 2010
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Submitted by w-henson.
C.Ward Henson (UIUC Math)
Gurarii's Banach space, part 2
Abstract: Today we'll prove the key amalgamation lemma for Banach spaces. This yields a complete description of the type spaces of the continuous theory T of Gurarii's space. Using the continuous version of Ryll-Nardzewski's Theorem we obtain Lusky's uniqueness theorem (= separable categoricity of T).

Tuesday, February 16, 2010

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, February 16, 2010
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Submitted by w-henson.
no meeting this week
Abstract: Urbana logicians will be going to the model theory day being organized at UIC; for details see the announcement at http://www.math.uic.edu/~alice/mwmtday.html