Seminar Calendar
for Logic Seminar events the year of Tuesday, August 7, 2012.

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events for the
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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 17, 2012

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, January 17, 2012
 Del Edit Copy
Submitted by phierony.
 Michael Tychonievich (Ohio State University)Metric Properties of Sets Definable in the Expansion of the Real Field by a Logarithmic SpiralAbstract: We discuss some metric properties of sets definable in certain expansions of the real field, including expansions of the real field by logarithmic spirals. For example, in these structures each bounded definable curve has finite length if and only if the dimension of its frontier is 0.

Tuesday, January 31, 2012

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, January 31, 2012
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Submitted by ssolecki.
 Dan Grayson (UIUC)Voevodsky's new foundations for mathematicsAbstract: Voevodsky's "Homotopy Type Theory" uses topology to provide new models for checking the consistency of a "type theory" close to what is currently implemented in the mathematical proof-checking computer program "coq". The new models allow the introduction of new axioms into the theory. These ideas promise to dramatically simplify the computerized checking of the proofs of modern mathematics, perhaps inaugurating the era where mathematicians commonly check their work as they proceed. In this talk a relative newcomer to the field will give an elementary account of the new theory and explain what it has to do with topology.

Tuesday, February 7, 2012

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, February 7, 2012
 Del Edit Copy
Submitted by ssolecki.
 Robert Kaufman (UIUC)Hurewicz's Theorem on Uncountable Close Sets--A DetourAbstract: When M is an uncountable, compact metric space the uncountable, closed subsets of M form an analytic, non-Borel set. We present a variant of this, relying on the notion of ultrametric space. Time permitting, we review the original proof, and suggest an alternative based on earlier work of Mazurkiewicz and Sierpin'ski.

Friday, February 17, 2012

Logic Seminar
4:00 pm   in 347 Altgeld Hall,  Friday, February 17, 2012
 Del Edit Copy
Submitted by ssolecki.
 Kostya Slutsky (UIUC)Two-sided invariant metrics on HNN extensionsAbstract: We discuss some technical properties of the Graev metrics on the free products of groups with two-sided invariant metrics and will sketch the construction of the the two-sided invariant metrics on HNN extensions of groups of bounded diameter.

Tuesday, February 21, 2012

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, February 21, 2012
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Submitted by ssolecki.
 Ward Henson (UIUC)Uncountably categorical Banach space structuresAbstract: Model theory is applied to (unit balls of) Banach spaces (and structures based on them) using the $[0,1]$-valued continuous version of first order logic. A theory $T$ of such structures is said to be $\kappa$-categorical if $T$ has a unique model of density $\kappa$. Work of Ben Yaacov and Shelah-Usvyatsov shows that Morley's Theorem holds in this context: if $T$ has a countable signature and is $\kappa$-categorical for some uncountable $\kappa$, then $T$ is $\kappa$-categorical for all uncountable $\kappa$. Known examples of uncountably categorical such structures are closely related to Hilbert space. After the speaker called attention to this phenomenon, Shelah and Usvyatsov investigated it and proved a remarkable result: if $M$ is a nonseparable Banach space structure (with countable signature) whose theory is uncountably categorical, then $M$ is prime over a Morley sequence that is an orthonormal Hilbert basis of length equal to the density of $M$. There is a wide gap between this result and verified examples of uncountably categorical Banach spaces, which leads to the question: can a stronger such result be proved, in which the connection to Hilbert space structure is clearly expressed in the geometric language of functional analysis? The main part of this talk will focus on some new examples of uncountably categorical Banach spaces that the speaker has studied. This is based on joint work with Yves Raynaud.

Tuesday, February 28, 2012

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, February 28, 2012
 Del Edit Copy
Submitted by ssolecki.
 Slawomir Solecki (Department of Mathematics, University of Illinois at Urbana-Champaign)Point realizations of Boolean actionsAbstract: I will show that if $M$ is an uncountable compact metric space, then there is an action of the Polish group of all continuous functions from $M$ to $U(1)$ on a separable probability algebra which preserves the measure and yet does not admit a point realization in the sense of Mackey. This is in contrast with Mackey's point realization theorem for locally compact, second countable groups. The proof of the above theorem goes through showing certain results concerning the infinite dimensional Gaussian measure space $({\mathbb C}^{\mathbb N},\gamma_\infty)$ which contrasts the Cameron--Martin Theorem. I will place the main result in the background of recent work on point realization and lack thereof for various classes of Polish groups. These results are due to Becker, Glasner, Tsirelson, Weiss, Kwiatkowska and myself. This is a joint work with Justin Moore.

Tuesday, March 6, 2012

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, March 6, 2012
 Del Edit Copy
Submitted by ssolecki.
 Lou van den Dries (Department of Mathematics, University of Illinois at Urbana-Champaign)The structure of approximate groups according to Breuillard, Green, TaoAbstract: Roughly speaking, an approximate group is a finite symmetric subset A of a group such that AA can be covered by a small number of left-translates of A. Last year the authors mentioned in the title established a conjecture of H. Helfgott and E. Lindenstrauss to the effect that approximate groups are finite-by-nilpotent''. This may be viewed as a sweeping generalisation of both the Freiman-Ruzsa theorem on sets of small doubling in the additive group of integers, and of Gromov's characterization of groups of polynomial growth. Among the applications of the main result are a finitary refinement of Gromov's theorem and a generalized Margulis lemma conjectured by Gromov. Prior work by Hrushovski on approximate groups is fundamental in the approach taken by the authors. They were able to reduce the role of logic to elementary arguments with ultra products. The point is that an ultraproduct of approximate groups can be modeled in a useful way by a neighborhood of the identity in a Lie group. This allows arguments by induction on the dimension of the Lie group. I will give two talks: the one on Tuesday will describe the main results, and the sequel on Friday will try to give a rough idea of the proofs.

Tuesday, March 13, 2012

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, March 13, 2012
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Submitted by ssolecki.
 Christian Rosendal (UIC)Global and local boundedness of Polish groupsAbstract: We present a comprehensive theory of boundedness properties for Polish groups developed with a main focus on Roelcke precompactness (precompactness of the lower uniformity) and Property (OB) (boundedness of all isometric actions on separable metric spaces). In particular, these properties are characterised by the orbit structure of isometric or continuous affine representations on separable Banach spaces or Hilbert space.

Tuesday, April 3, 2012

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, April 3, 2012
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Submitted by phierony.
 Robert E. Jamison (Clemson/UIUC)A Dependency Calculus for Finitary ClosuresAbstract: A closure system consists of a ground set $X$ together with a family $\mathscr{C}$ of closed subsets of $X$. The only requirements are that $\mathscr{C}$ is closed under arbitrary intersections and contains $X$. Thus each subset $S$ of $X$ lies in a smallest closed set $\mathscr{C}(S)$. The map $S \to \mathscr{C}(S)$ is the closure operator. The closure operator is finitary provided whenever $p \in \mathscr{C}(S)$, there is a finite subset $E$ of $S$ with $p \in \mathscr{C}(E)$. In this talk a first order logic for finitary closure operators will be presented. This first order logic can be used to describe and systematize the study of most important properties of finitary systems. In particular, I will describe a classification scheme for many of the important classes of finitary closures (matroids, antimatroids, partial order convexity, etc). Moreover, I will describe several metatheorems concerning classical convexity invariants such as the Helly and Radon numbers.

Tuesday, April 10, 2012

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, April 10, 2012
 Del Edit Copy
Submitted by ssolecki.
 Slawomir Solecki (Department of Mathematics, University of Illinois at Urbana-Champaign)Abstract approach to Ramsey theory and Ramsey theorems for finite treesAbstract: I will show how certain Ramsey results for finite trees (some old, some new) are obtained by applying an abstract approach to Ramsey theory. A streamlined version of this abstract approach will be explained in the talk.

Friday, April 20, 2012

Logic Seminar
4:00 pm   in 347 Altgeld Hall,  Friday, April 20, 2012
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Submitted by ssolecki.
 Dana Bartosova (University of Toronto)Universal minimal flows in the language of filtersAbstract: I will introduce a construction by Balcar and Franek of the Boolean algebra of clopen sets of the universal minimal dynamical system for discrete groups. I will show how that generalizes to topological groups. I will talk about a couple of applications of this approach, e.g. to groups of automorphisms of uncountable structures using methods of Kechris, Pestov and Todorcevic connecting structural Ramsey theory and topological dynamics.

Tuesday, April 24, 2012

Logic Seminar
1:00 pm   in Altgeld Hall,  Tuesday, April 24, 2012
 Del Edit Copy
Submitted by ssolecki.
 Anush Tserunyan (UCLA)Finite generators for countable group actionsAbstract: Consider a Borel action of a countable group $G$ on a standard Borel space $X$. A countable Borel partition $P$ of $X$ is called a generator if $GP=\{ gA: g \in G, A \in P\}$ generates the Borel $\sigma$-algebra of $X$. Existence of such $P$ of cardinality $n$ is equivalent to the existence of a $G$-embedding of $X$ into the shift $n^G$. For $G=Z$, the Kolmogorov-Sinai theorem implies that finite generators don't exist in the presence of an invariant probability measure with infinite entropy. It was asked by Weiss in the late 80s, whether the nonexistence of any invariant probability measure would guarantee the existence of a finite generator. We show that the answer is positive in case $X$ admits a $\sigma$-compact topological realization (e.g. if $X$ is a $\sigma$-compact Polish $G$-space). We also show that finite generators always exist in the context of Baire category thus answering a question of Kechris. In fact, we show that if $X$ is a Polish $G$-space having infinite orbits, then there is a 4-generator on an invariant comeager set.

Friday, April 27, 2012

Logic Seminar
4:00 pm   in 347 Altgeld Hall,  Friday, April 27, 2012
 Del Edit Copy
Submitted by phierony.
 Eva Leenknegt (Purdue)In search of p-adic minimality: An exploration of weak p-adic structuresAbstract: Consider a structure (F,L), where F is a field and L is a language that is 'related' to the language of rings, in the sense that the Lring-definable subsets of F coincide with the L-definable subsets of F (that is, we require (F,L) to be 'Lring-minimal'). When F is a real closed field, a structure satisfying this property will be o-minimal, so all tools of o-minimality, such as the cell decomposition theorem, are at our disposal when studying such structures. The situation is less clear when F is a p-adic(ally closed) field. If L is an expansion of the ring languages, then (F,L) will be P-minimal, but very little is known in general for weaker structures (reducts of the ring language) When will a reduct L of the ring language give rise to an Lring-minimal structure? In the o-minimal case, the answer is easy: the only requirement is that the order should be definable in L. Our first challenge will be to find a p-adic equivalent of this 'minimal language' (<). Once such a language has been found, one can start constructing examples of weak p-adic Lring- minimal structures. While a general theory is still far away, individual examples show that there are some fundamental differences when comparing p-adic and o-minimal reducts of the ring language. I will give some examples of this. One of the questions that comes up is the existence of cell decomposition: could it possibly be true that every p-adic Lring-minimal language has cell decomposition? I will discuss some (partial) answers to this question, and show how we can use this to study examples of weak structures.

Tuesday, May 1, 2012

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, May 1, 2012
 Del Edit Copy
Submitted by ssolecki.
 Laurentiu Leustean (Institute of Mathematics of the Romanian Academy)Proof mining in nonlinear analysisAbstract: The program of proof mining is concerned with the extraction of hidden finitary and combinatorial content from proofs that make use of highly infinitary principles. This new information can be both of quantitative nature, such as algorithms and effective bounds, as well as of qualitative nature, such as uniformities in the bounds or weakening the premises. Thus, even if one is not particularly interested in the numerical details of the bounds themselves, in many cases such explicit bounds immediately show the independence of the quantity in question from certain input data. This line of research, developed by Ulrich Kohlenbach in the 90's, has its roots in Georg Kreisel's program on unwinding of proofs, put forward in the 50's. In this talk I will present applications of proof mining to the asymptotic behavior of nonexpansive iterations and nonlinear generalizations of ergodic averages.

Tuesday, September 4, 2012

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, September 4, 2012
 Del Edit Copy
Submitted by phierony.
 Andrew Arana (UIUC Philosophy & Math)Transfer in algebraic geometryAbstract: The focal question of this talk is to investigate the value of transfer between algebra and geometry, of the sort exemplified by the Nullstellensatz. Algebraic geometers frequently talk of such transfer principles as a "dictionary" between algebra and geometry, & claim that these dictionaries are fundamental to their practice. We'll first need to get clear on what such transfer consists in. We'll then investigate what how such transfer might improve how knowledge is gathered in algebraic geometric practice.

Tuesday, September 11, 2012

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, September 11, 2012
 Del Edit Copy
Submitted by phierony.
 Andrew Arana (UIUC Philosophy and Math)Transfer in algebraic geometry - Part IIAbstract: The focal question of this talk is to investigate the value of transfer between algebra and geometry, of the sort exemplified by the Nullstellensatz. Algebraic geometers frequently talk of such transfer principles as a "dictionary" between algebra and geometry, & claim that these dictionaries are fundamental to their practice. We'll first need to get clear on what such transfer consists in. We'll then investigate what how such transfer might improve how knowledge is gathered in algebraic geometric practice. --- This talk is a continuation of the talk given in the Logic seminar last week. Enough of a survey of what has come before will be given so that people who missed the first talk, can still attend this talk with profit.

Tuesday, September 18, 2012

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, September 18, 2012
 Del Edit Copy
Submitted by phierony.
 Mia Minnes (UC San Diego)Algorithmic Randomness via Random AlgorithmsAbstract: Algorithmic randomness defines what it means for a single mathematical object to be random. This active area of computability theory has been particularly fruitful in the past several decades, both in terms of expanding theory and increasing interaction with other areas of math and computer science. Randomness can be equivalently understood in terms of measure theory, descriptive complexity, and martingales. In this context, we present a novel definition of betting strategies that uses probabilistic algorithms also studied in complexity theory. This definition leads to new characterizations of several central notions in algorithmic randomness and addresses Schnorr's critique, a longstanding philosophical question in algorithmic randomness. Moreover, these techniques suggest new approaches for tackling one of the biggest open questions in the field (KL = ML?). This is joint work with Sam Buss.

Thursday, October 11, 2012

Logic Seminar
1:00 pm   in 243 Altgeld Hall,  Thursday, October 11, 2012
 Del Edit Copy
Submitted by ssolecki.
 Marcin Sabok (Polish Academy of Sciences)Canonization for equivalence relations classifiable by countable structuresAbstract: I will discuss several results on canonical Ramsey theory in the context of descriptive set theory. I will focus on Borel equivalence relations which are classifiable by countable structures and show what kind of canonization results can be obtained for this class. Canonization in this class will turn out to be closely related to canonization in the smaller class of essentially countable equivalence relations.

Friday, October 12, 2012

Logic Seminar
3:00 pm   in 347 Altgeld Hall,  Friday, October 12, 2012
 Del Edit Copy
Submitted by phierony.
 Isaac Goldbring (UIC)The theory of tracial von Neumann algebras does not have a model companionAbstract: In this talk, we will show that the theory of tracial von Neumann algebras does not have a model companion. In addition, we will show that a positive solution to the Connes Embedding Problem implies that there is no model complete theory of tracial von Neumann algebras. All functional analytic notions and most model-theoretic notions will be defined. This is joint work with Bradd Hart and Thomas Sinclair.

Tuesday, October 16, 2012

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, October 16, 2012
 Del Edit Copy
Submitted by ssolecki.
 Dima Sinapova (UIC)The Singular Cardinal Problem and Prikry ForcingsAbstract: The Singular Cardinal Problem is the problem to completely describe the behavior of the operation $\kappa\mapsto 2^\kappa$ restricted to singular cardinals. Dealing with this problem involves constructing various models where the Singular Cardinal Hypothesis (SCH) fails. This is done using Prikry type forcings in the context of large cardinals. I will give some background on the subject and then go over some resent consistency results about the relationship between SCH and weak square.

Tuesday, October 23, 2012

Logic Seminar
1:00 pm   in UIC, SEO 636,  Tuesday, October 23, 2012
 Del Edit Copy
Submitted by phierony.
 Midwest Model Theory DayAbstract: Midwest Model Theory Day at UIC. The speakers are Lynn Scow, Isaac Goldbring and Maryanthe Malliaris. For details, see http://www.math.wisc.edu/~andrews/MWMTD5.html

Tuesday, October 30, 2012

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, October 30, 2012
 Del Edit Copy
Submitted by ssolecki.
 Min Zhao (UIUC )A self-dual Ramsey theorem for Spencer's space and an abstract approach to Ramsey theoryAbstract: First, we will discuss the abstract approach to Ramsey theory and the self-dual Ramsey theorem for partitions developed by Solecki. Then we will introduce the Ramsey theorem for Spencer's space developed by Spencer. After that, by applying the abstract approach, we will give a self-dual Ramsey theorem for Spencer's spaces, which is a generalization of the self-dual Ramsey theorem for partitions.

Tuesday, November 6, 2012

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, November 6, 2012
 Del Edit Copy
Submitted by phierony.
 Philipp Hieronymi (UIUC Math)Dimension coincidence for expansions of the real fieldAbstract: I will report on joint work with Chris Miller on the question when in expansions of the real field Minkowski dimension and Euclidean dimension coincide.

Tuesday, November 13, 2012

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, November 13, 2012
 Del Edit Copy
Submitted by phierony.
 Tobias Kaiser (Universität Passau)A very fi rst step towards an algebraic understanding of the ring of analytic functions that are globally subanalyticAbstract: We are interested in the ring of functions that are analytic and globally subanalytic on a given globally subanalytic domain. The motivation comes from the following two results: The ring of functions that are analytic on a neighbourhood of a compact subanalytic set is Noetherian (see [J. Frisch: Points de platitude d'un morphisme d'espaces analytiques complexes, Inventiones math. 4, 118-138 (1967)]) and the ring of Nash functions (i.e. functions that are analytic and semialgebraic) on a semialgebraic domain is Noetherian (see [J.-J. Risler: Sur l'anneau des fonctions de Nash globales, Ann. Sci. Ecole Norm. Sup. 8, 365-378 (1975)]). To deal with the rings in the subanalytic case it is natural to try rst to understand the local rings given by germs at boundary points of the domain. The most promising tool for that is the rectilinearization theorem proven by Bierstone& Milman and Parusinski. There rings of multivariate Puiseux series comes into the game. We describe these rings as twisted group rings.