Seminar Calendar
for Topology Seminar events the next 12 months of Wednesday, August 1, 2012.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
      July 2012             August 2012           September 2012
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  6  7             1  2  3  4                      1
8  9 10 11 12 13 14    5  6  7  8  9 10 11    2  3  4  5  6  7  8
15 16 17 18 19 20 21   12 13 14 15 16 17 18    9 10 11 12 13 14 15
22 23 24 25 26 27 28   19 20 21 22 23 24 25   16 17 18 19 20 21 22
29 30 31               26 27 28 29 30 31      23 24 25 26 27 28 29
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Thursday, August 30, 2012

2:00 pm   in 241 Altgeld Hall,  Thursday, August 30, 2012
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Submitted by collier3.
 Informational and Organizational meetingAbstract: It's time for the graduate geometry and topology seminar to start again. We will meet for a short organizational meeting. Everyone in strongly encouraged to attend, especially new first years. COOKIES will be provided.

Tuesday, September 4, 2012

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, September 4, 2012
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Submitted by franklan.
 Jim McClure (Purdue University)Verdier duality and Poincare dualityAbstract: There is a well-known argument that deduces Poincare duality from Verdier duality. In the lecture I will review the relevant sheaf-theoretic background and show that the isomorphism obtained in this way is the same as the classical isomorphism obtained from the cap product. As a byproduct I will observe that Verdier duality is not actually needed for the well-known argument mentioned above. Everything I will say has an analogue for intersection homology (in particular, Verdier duality is not needed for the proof of Poincare duality in that situation either); I'll say something about this at the end if time allows.

Thursday, September 6, 2012

2:00 pm   in 241,  Thursday, September 6, 2012
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Submitted by collier3.
 Anton Lukyanenko (UIUC Math)What is geometric group theory and who cares?Abstract: How do you tell if two groups are isomorphic? This is an extremely difficult task, but in certain cases attaching geometric notions to the groups makes it tractable and leads to new, intriguing geometries. The main example will come from the Heisenberg group, which with a (sub-)Riemannian metric becomes one of the 8 Thurston geometries.

Tuesday, September 11, 2012

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, September 11, 2012
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Submitted by franklan.
 Ben Ward (Purdue University)From pre-Lie to BVAbstract: We will investigate several extensions of the notion of an operad and consider algebraic structures encoded by and arising from them, including (pre-)Lie, Frobenius, Gerstenhaber and BV structures. Then, motivated by topological questions, we will study the example of $A_{\infty}$ Frobenius algebras and the associated BV (resp. homotopy BV) structure on the Hochschild cohomology (resp. cochains). This is partially joint work with Ralph Kaufmann and Javier Zuniga.

Thursday, September 13, 2012

2:00 pm   in 241 Altgeld Hall,  Thursday, September 13, 2012
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Submitted by collier3.
 Peter Nelson (UIUC Math)What is a (co)homology theory and why you should care.Abstract: The main goal of algebraic topology is to study spaces via various algebraic invariants. I'll give a brief introduction to the primary type of these invariants, namely, homology and cohomology theories. Examples and "geometric" applications will abound.

Tuesday, September 18, 2012

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, September 18, 2012
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Submitted by franklan.
 Sean Tilson (Wayne State University)Power operations and the Kunneth Spectral SequenceAbstract: Power operations have been constructed and successfully utilized in the Adams and Homological Homotopy Fixed Point Spectral Sequences by Bruner and Bruner-Rognes. It was thought that such results were not specific to the spectral sequence, but rather that they arose because highly structured ring spectra are involved. In this talk, we show that while the Kunneth Spectral Sequence enjoys some nice multiplicative properties, the obvious algebraic operations are zero (other than the square). Despite the negative results we are able to use old computations of Steinberger's with our current work to compute operations in the homotopy of some relative smash products.

Thursday, September 20, 2012

2:00 pm   in 241 Altgeld Hall,  Thursday, September 20, 2012
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Submitted by collier3.
 Mike DiPasquale (UIUC Math)Bezout, Cayley-Bacharach, and PascalAbstract: We introduce some basic constructions of algebraic geometry in the process of exploring the geometry of curves in the complex projective plane. In particular we will discuss Bezout's theorem and the Cayley-Bacharach theorem for plane cubics, pointing out the special case of Pascal's 'mystic hexagon.' The object is to communicate the power of algebraic machinery in proving some beautiful geometric theorems.

Tuesday, September 25, 2012

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, September 25, 2012
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Submitted by franklan.
 David Gepner (Universität Regensburg)Brauer groups of commutative ring spectraAbstract: The Picard and Brauer groups of a commutative ring spectrum R can be interpreted as the first two negative homotopy groups of a nonconnective version of the spectrum of units of R. We'll focus on two techniques for computing these negative homotopy groups: if R is connective, then any Azumaya R-algebra is etale locally trivial, and these groups reduce to the etale cohomology of the sheaf of units $GL_1$; if R is nonconnective, then this probably fails, but nevertheless R often admits interesting finite G-Galois extensions whose group cohomology computes the relative Picard and Brauer groups. This is joint work with B. Antieau and T. Lawson, respectively.

Thursday, September 27, 2012

2:00 pm   in 241 Altgeld Hall,  Thursday, September 27, 2012
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Submitted by collier3.
 Bill Karr (UIUC Math)Geodesics on Surfaces of Revolution in Minkowski SpaceAbstract: I will introduce some basic definitions from Lorentzian geometry and a notion of angle in the tangent space to a Lorentzian manifold. Then, I'll explain my REGS project about geodesics on surfaces of revolution in Minkowski space using a spacetime version Clairaut's relation from classical differential geometry.

Tuesday, October 2, 2012

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, October 2, 2012
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Submitted by franklan.
 Inna Zakharevich (University of Chicago)Ring structures on scissors congruence spectraAbstract: Hilbert's third problem asks the following question: given two polyhedra, when is it possible to dissect them into a finite number of pairwise congruent polyhedra? The answer, given by the Dehn-Sydler theorem (1901,1965) is that it is possible whenever two invariants -- the volume and the Dehn invariant -- are equal. Generalizing this problem, we can say that two polytopes in a nice enough manifold (such as $R^n$, $S^n$, or $H^n$) are "scissors congruent" if they can be dissected into a finite number of pairwise congruent polytopes and ask for a classification of scissors congruence types. This question was studied by Dupont and Sah, who assigned groups of scissors congruence types on manifolds and analyzed many structures on these groups. In particular, it turns out that in the case of $E^n$ and $S^n$, the groups assemble into a graded ring. In this talk we give a different perspective on scissors congruence groups by showing that they arise as the 0-th K-group of a particular type of Waldhausen category, and use Dupont and Sah's observations to construct these ring structures directly on the K-theoretic level.

Thursday, October 4, 2012

2:00 pm   in 241 Altgeld Hall,  Thursday, October 4, 2012
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Submitted by collier3.
 Sarah Yeakel (UIUC Math)What is Calculus of Functors?Abstract: Functors between categories give a wealth of information, but can be extremely complicated to compute. We teach our calculus students to approximate difficult real valued functions with polynomials. This technique can be applied to categories we know and love to produce some awesome results. I'll talk about some basic examples of functors on topological spaces and how the theory can be used on manifolds and vector spaces as well.

Tuesday, October 9, 2012

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, October 9, 2012
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Submitted by franklan.
 Marc Hoyois (Northwestern University)From algebraic cobordism to motivic cohomologyAbstract: I will present a famous theorem due to Hopkins and Morel which characterizes motivic cohomology of schemes as the universal oriented cohomology theory with additive formal group law. The talk will serve as a gentle introduction to motivic homotopy theory, geared towards understanding the statement of the theorem and some of its stunning applications.

Thursday, October 11, 2012

2:00 pm   in Altgeld Hall,  Thursday, October 11, 2012
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Submitted by collier3.
 Mychael Sanchez (UIUC Math)Homotopy theory and infinity categoriesAbstract: I'll talk about several objects of interest in homotopy theory, some properties they share, and some deficiencies of ordinary category theory when studying them. I'll then discuss a class of mathematical objects called infinity categories that correct some these deficiencies and how we might come up with them.

Tuesday, October 16, 2012

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, October 16, 2012
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Submitted by franklan.
 Anthony Elmendorf (Purdue University Calumet)Generalized and equivariant multicategoriesAbstract: Leinster developed a general procedure for defining multicategories using monads satisfying a Cartesian property. However, his definition only captures the usual notion of multicategory in the case when the multicategory doesn't have a symmetric structure. By looking at additional structure available when we start with a general $\Sigma$-free operad in Cat, we can account for the symmetric structure, and thereby generalize Leinster's construction to this case. The construction also easily accounts for the sort of equivariant operads considered by Guillou, May, and Merling in their ongoing study of equivariant infinite loop space theory via equivariant permutative categories. There are several natural conjectures that we will discuss.

Thursday, October 18, 2012

2:00 pm   in 241 Altgeld Hall,  Thursday, October 18, 2012
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Submitted by collier3.
 Seth Wolbert (UIUC Math)Stacks in Differential GeometryAbstract: A stack over the category of smooth manifolds is a structure that can be used to generalize the deconstructive (i.e., via restriction) and reconstructive (i.e.,via gluing) properties seen in fiber bundles. This talk is designed to give a gentle introduction to these structures and some of their nice properties. Given time, we will also discuss the stack of transport functors and how parallel transport induces an equivalence of categories between this stack and the stack of principal G-bundles with connections.

Tuesday, October 23, 2012

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, October 23, 2012
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Submitted by franklan.
 Agnes Beaudry (Northwestern University)The K(2)-local Moore spectrum at the prime 2Abstract: We use methods of Goerss, Henn, Karamanov, Mahowald, and Rezk to study the homotopy $\pi_*L_{K(2)}V(0)$ at the prime 2. In particular, we study the $E_2$-page of an Adams-Novikov spectral sequence converging to $\pi_*L_{K(2)}V(0)$ via another spectral sequence called the short resolution spectral sequence. Its $E_1$-page is composed of cohomology groups $H^n(G_k, (E_2)_*V(0))$ where $(E_2)_*$ is Morava $E$-theory and the $G_k$'s are finite subgroups of the Morava stabilizer group $\mathbb{G}_2$. These finite groups come from automorphisms of elliptic curves and we use the geometry thus made available to us to simplify computations. We explain how to obtain the $E_2$-page of the short resolution spectral sequence for $(E_2)_*V(0)$ and compute the complete spectral sequence for $v_1^{-1}(E_2)_*V(0)$. This gives the $E_2$-page of the Adams-Novikov spectral sequence, namely $H^*(\mathbb{G}_2, v_1^{-1}(E_2)_*V(0))$. We expect the differentials to follow classical patterns and explain what this would imply for $v_1^{-1}\pi_*L_{K(2)}V(0)$.

Thursday, October 25, 2012

2:00 pm   in 241 Altgeld Hall,  Thursday, October 25, 2012
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Submitted by collier3.
 Nathan Rehfuss (UIUC MATH)The Unknot and Why You Should Care.Abstract: I plan to give a brief general overview of knot theory, followed by an exploration of the methods, challenges, and applications of the unknotting problem.

Tuesday, October 30, 2012

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, October 30, 2012
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Submitted by franklan.
 Matthew Thibault (University of Chicago)Finite simplicial complexes via pro-posetsAbstract: One has a pair of functors between finite topological spaces and finite simplicial complexes. Via this correspondence, McCord proves that finite topological spaces up to weak homotopy equivalence coincides with finite simplicial complexes up to homotopy equivalence. Since finite topological spaces coincide with finite posets, this allows one to convert problems in algebraic topology into problems in combinatorics. However, due to a dearth of maps in the category of finite spaces, one must enlarge this category in order to describe all homotopy classes of maps between (finite) simplicial complexes. In this talk, I will describe the homotopy category of finite simplicial complexes in terms of the category of pro-posets.

Wednesday, October 31, 2012

Special Topology Seminar
4:00 pm   in 145 Altgeld Hall,  Wednesday, October 31, 2012
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Submitted by franklan.
 Irakli Patchkoria (Universität Bonn)Rigidity in equivariant stable homotopy theoryAbstract: Let G be a finite abelian group or finite (non-abelian) 2-group. We show that the 2-local G-equivariant stable homotopy category, indexed on a complete G-universe, has a unique G-equivariant model in the sense of Quillen model categories. This means that the suspension functor, homotopy cofiber sequences and the stable Burnside category determine all "higher order structure" of the 2-local G-equivariant stable homotopy category such as for example equivariant homotopy types of function G-spaces. The theorem can be seen as an equivariant generalization of Schwede's rigidity theorem at the prime 2.

Thursday, November 1, 2012

2:00 pm   in 241 Altgeld Hall,  Thursday, November 1, 2012
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Submitted by collier3.
 Juan Villeta-Garcia (UIUC Math)Beginner Intersection Theory in Algebraic GeometryAbstract: Given two varieties V and W in \mathbb{P}^n, understanding their intersection V\cap W has been a subject of constant research for most of the 20th century. Many definitions of what an intersection product should be have been given, and subsequently refined. We will give a gentle introduction from the algebraic approach, but also incorporate such constructions as Chern classes and Chow Rings, if time permits. We will have lots of examples!

Tuesday, November 6, 2012

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, November 6, 2012
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Submitted by franklan.
 Jim Davis (Indiana University)Every finite group acts freely and homologically trivially on a product of spheresAbstract: I show that if K is a finite CW complex with finite fundamental group G and universal cover homotopy equivalent to $X=S^{n_1} \times \ldots \times S^{n_k}$, then for every $n \geq dim X$, G acts freely on $X \times S^n$, with the action on homology given by $g \otimes 1 \colon H_*(X) \otimes H_*(S^n) \to H_*(X) \otimes H_*(S^n)$. Recently Unlu and Yalcin constructed for any finite group G, a finite CW complex K with universal cover homotopy equivalent to a product of spheres, where G acts trivially on the homology of the universal cover of K. As a corollary we get the title of the talk.

Thursday, November 8, 2012

2:00 pm   in 241 Altgeld Hall,  Thursday, November 8, 2012
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Submitted by collier3.
 (UIUC Math)Abstract: Cancelled this week. Go to women's seminars instead.

Tuesday, November 13, 2012

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, November 13, 2012
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Submitted by franklan.
 Jonathan Campbell (Stanford University)Topological Hochschild homology and Koszul dualityAbstract: Topological Hochschild homology (THH) is an invariant of ring spectra related both to K-theory and topological field theories. In this talk I'll state and prove a theorem concerning the relationship between THH and Koszul duality. I'll introduce the necessary definitions, and in particular say what I mean by "Koszul duality". I will also introduce some $\infty$-categorical background that will be necessary for the proof. Finally, I'll discuss some related results that I believe to be true, and applications of the work above to topological field theories.

Thursday, November 15, 2012

2:00 pm   in 241 Altgeld Hall,  Thursday, November 15, 2012
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Submitted by collier3.
 Brian Collier (UIUC Math)Flat Bundles and Representations of the Fundamental Group.Abstract: Given a manifold $M$ and a vector space V, a representation $\rho:\pi_1(M)\rightarrow GL(V)$ gives rise to a flat vector bundle via associated bundles and the action of $\pi_1(M)$ on the universal cover. Conversely given a vector bundle with a flat structure we get a representation of $\pi_1(M)$. To appreciate this correspondence we will need to discuss some general bundle theory and flat structures this will be done through many examples. This talk should be accessible to all graduate students interested in geometry.

Tuesday, November 27, 2012

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, November 27, 2012
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Submitted by franklan.
 Lena Folwaczny (University of Illinois at Chicago)New constructions of virtual knot polynomialsAbstract: Virtual knots and links can be described topologically as embeddings of circles in thickened surfaces (of arbitrary genus) taken up to surface homeomorphisms and 1-handle stabilization. In this talk we give an alternate definition of a virtual knot polynomial, the Affine Index Polynomial, using virtual linking numbers. We call this new definition the Wriggle Polynomial. The Affine Index Polynomial is defined in terms of an integer labeling system of a virtual knot diagram that derives from an essentially unique structure of an affine flat biquandle for flat virtual diagrams, and equality of the definitions is not immediately obvious. Interesting applications of this polynomial to Vassiliev Invariants, Mutant Knots, and the Cosmetic Crossing Change Conjecture are discussed.

Thursday, November 29, 2012

2:00 pm   in 241 Altgeld Hall,  Thursday, November 29, 2012
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Submitted by collier3.
 Nerses Aramian (UIUC Math)Milnor's Exotic SphereAbstract: In 1956 Milnor constructed an example of a differentiable manifold that is homeomorphic to $S^7$, but is not diffeomorphic to it. The existence of such an object is quite remarkable, since it shows that not everything about a manifold is determined by its topological structure. In fact, later it was shown that for the case of spheres it is a rare phenomenon to have a unique differentiable structure. I am going to attempt to walk you through the construction of the exotic $S^7$. As the discussion progresses there will be a need to introduce several tools, such as Poincare Duality, Oriented Bordism, Pontrjagin Classes, Hirzebruch Signature Formula. I will attempt to make some of the discussion more homotopical'', so as to convince you that homotopy theory may provide a gateway to generalizations of Milnor's argument.

Tuesday, December 4, 2012

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, December 4, 2012
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Submitted by franklan.
 Stephan Stolz (University of Notre Dame)2-dimensional field theories and modular formsAbstract: Graeme Segal suggested two decades ago that the generalized cohomology theory now known as "Topological Modular Form Theory" of a manifold X should be related to families of 2-dimensional field theories parametrized by X. This is an analog of the well-known statement that homotopy classes of families of Fredholm operators parametrized by X can be identified with the K-theory of X. In this talk on joint work with Peter Teichner, I will present a conjectural picture of TMF(X) as concordance classes of families of supersymmetric 2-dimensional Euclidean field theories parametrized by X. Evidence for the conjecture comes from an analogous description of K(X) in terms of 1-dimensional field theories, and our result that the partition function of a supersymmetric 2-dimensional Euclidean field theory is a modular form. The latter is the main focus of the talk.

Thursday, December 6, 2012

2:00 pm   in 241 Altgeld Hall,  Thursday, December 6, 2012
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Submitted by collier3.
 Daniel Hockensmith (UIUC Math)An Introduction to JetsAbstract: What is a jet bundle and how does one use it? One expects multiple answers to the latter question, but it is somewhat surprising that there are also multiple answers to the former. We will highlight one approach to jet bundles and apply it to the study of PDE's. In the process, we will discover relationships between geometric objects (i.e. curvature of connections on a fiber bundle) and historically analytic objects (i.e. PDE's and their solutions). Our focus will be placed upon the first jet bundle as there is a plethora of readily visualized examples, but we will certainly talk about jet bundles of arbitrary finite order.

Tuesday, December 11, 2012

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, December 11, 2012
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Submitted by franklan.
 John Harper (Purdue University)TQ-homology completion of nilpotent structured ring spectraAbstract: An important theme in current work in homotopy theory is the investigation and exploitation of enriched algebraic structures on spectra that naturally arise, for instance, in algebraic topology, algebraic K-theory, and derived algebraic geometry. Such structured ring spectra or geometric rings'' are most simply viewed as algebraic-topological generalizations of the notion of ring from algebra and algebraic geometry. This talk will describe recent progress, in joint work with M. Ching, on developing standard tools of the homotopy theory of spaces in this new algebraic-topological context of structured ring spectra, with a special emphasis on recovering algebraic and topological structures from associated homology objects.

Thursday, December 13, 2012

12:00 pm   in 241 Altgeld Hall,  Thursday, December 13, 2012
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Submitted by collier3.
 Ser-Wei Fu (UIUC Math)Geometry of Quadratic DifferentialsAbstract: Quadratic differentials have an intimidating name. Also the fact that it came from complex analysis has scared off people. I will introduce a very geometric way of describing the space, by semi-translation structures. The talk will be accessible by anyone who knows what a polygon is. The (impossible) goal is to give connections to the fields studied by the GEAR (GEometric structures And Representation varieties) network: Higgs Bundles, Teichmuller Spaces, Dynamics, Represenations, and 3-manifolds.

Thursday, January 17, 2013

2:00 pm   in 241 Altgeld Hall,  Thursday, January 17, 2013
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Submitted by collier3.
 Caglar Uyanik (UIUC Math)Mapping Class Groups and Automorphisms of Free GroupsAbstract: This will be an introductory talk about how to understand Mapping Class Groups and Automorphisms of Free Groups. Along the way, we will define and talk about hyperbolic structures, measured laminations, geodesic currents, intersection form and Teichmuller Space. At the end, we will talk about how one can relate certain free group automorphisms to Mapping Class Groups and use this relation and geometric topology to prove theorems in group theory.

Tuesday, January 22, 2013

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, January 22, 2013
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Submitted by franklan.
 Eric Peterson (UC Berkeley)Cotangent spaces for certain spectraAbstract: We outline a construction in derived algebraic geometry which produces elements of the K(n)-local Picard group. As an example, we produce a new model of a spectrum called the determinantal sphere, and as time permits we discuss some newly indicated patterns in K(n)-local homotopy theory.

Thursday, January 24, 2013

2:00 pm   in 241 Altgeld Hall,  Thursday, January 24, 2013
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Submitted by collier3.
 Noel DeJarnette (UIUC Math)Horseshoes, Hand Grenades, and subRiemannian ManifoldsAbstract: We will explore approximation techniques seen in subRiemannian Geometry: Nilpotentization and penalty metrics specifically. We will build these techniques through examples on the Grusin Plane, Heisenberg Group, and the Engel Group. Through these examples we will also see when these techniques should be applied and what they are telling us.

Tuesday, January 29, 2013

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, January 29, 2013
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Submitted by franklan.
 Justin Noel (Universität Bonn)Maps of homotopy T-algebrasAbstract: If T is a (nice) monad acting on a (very nice) model category C we obtain a (nice) model category of T-algebras in C. Moreover, the monad T descends in this situation to a monad T' in the homotopy category of C and we have a forgetful functor from the derived category of T-algebras to T'-algebras in hoC. In the case that C is spectra and T-algebras in C are $E_\infty$ ring spectra, this forgetful functor lands in $H_\infty$ ring spectra. To analyze this functor, Niles Johnson and I constructed a spectral sequence which computes the homotopy of the space of T-algebra maps and whose edge homomorphism is this forgetful functor. A number, hopefully greater than zero, of examples will be given. These examples connect to rational unstable homotopy theory, chromatic theory and Coker J, equivariant homotopy theory, and realization questions in algebra.

Thursday, January 31, 2013

2:00 pm   in 241 Altgeld Hall,  Thursday, January 31, 2013
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Submitted by collier3.
 Sean Shahkarami (UIUC Math)Duality Among Central Forces (and Kepler's First Law as an Example!)Abstract: Kepler's laws of motion describe the orbit of a planet undergoing an inverse-square gravitational force. In particular, the first law tells us that bounded orbits trace out ellipse with one of their foci at the center of the force. I'd like to describe a neat, geometric (but seemingly less well known) alternative to the usual derivation of this law and show how this approach leads to a general duality between central force systems and their orbits.

Tuesday, February 5, 2013

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, February 5, 2013
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Submitted by franklan.
 Donald Yau (Ohio State University at Newark)To infinity-properads and beyondAbstract: Properads are more general operational structures than operads in the sense that operations with multiple inputs and multiple outputs are allowed. I will describe a homotopy version of properads, called infinity-properads, that extend both infinity-categories in the sense of Joyal-Lurie and infinity-operads in the sense of Cisinski-Moerdijk-Weiss.

Thursday, February 7, 2013

2:00 pm   in 241 Altgeld Hall,  Thursday, February 7, 2013
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Submitted by collier3.
 Yasten Wong (UIUC Math)A short introduction to J-holomorphic curveAbstract: The notion of J-holomorphic curve was introduced by Gromov in 1985, it is defined as a mapping from a Riemann surface to an almost complex manifold satisfying the Cauchy-Riemann equation. It turns out that this notion made a big impact in the study of symplectic manifolds. In this talk I would like to describe some basic properties of J-holomorphic curve and show how Gromov uses them to prove his celebrated non-squeezing theorem.

Tuesday, February 12, 2013

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, February 12, 2013
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Submitted by franklan.
 David White (Wesleyan University)Model categories, algebras over operads, and Bousfield localizationAbstract: I'll discuss monoidal model categories and list a number of known results regarding model structures on the subcategories of monoids, commutative monoids, and algebras over more general operads. I'll then collect these results into a unified framework and as a corollary obtain a theorem which yields model structures on algebras over levelwise cofibrant operads. Examples and applications will be given. I came across this result as a part of a larger project to understand when Bousfield localization preserves strict commutative monoids. Time permitting, I'll explain the status of that project and my plans for the future.

Thursday, February 14, 2013

2:00 pm   in 241 Altgeld Hall,  Thursday, February 14, 2013
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Submitted by collier3.
 Olabode Sule (UIUC Physics)Chern Simons Theory and Group CohomologyAbstract: In a remarkable paper in 1989 Edward Witten conjectured using physics techniques that a quantum field theory (Chern-Simons) theory can be used to compute the Jones Polynomial invariants of knots in S^3. This construction has been placed on a quite rigorous footing using combinatorial methods by Reshetikhin, Turaev et al. It is generally believed that Chern-Simons theory is an example of a topological quantum field theory satisfying the axioms of Attiyah. In physics Chern-Simons theory plays a role in several places such as being an effective theory for the quantum hall states of matter. In my talk I will motivate, using physics examples, a discussion of aspects of quantum field theory (without going into details about quantization). I will focus on a discussion of the choice of an action and explain how the cohomology of groups play a role in defining an action for Chern Simons theory for compact Lie groups on any compact oriented 3-manifold.

Tuesday, February 19, 2013

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, February 19, 2013
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Submitted by franklan.
 Kate Ponto (University of Kentucky)Multiplicativity of fixed point invariantsAbstract: For a fibration (with a connected base space) the Euler characteristic of the total space is the product of the Euler characteristics of the base and fiber. If the fibration satisfies restrictive additional hypotheses this extends to generalizations of the Euler characteristic such as the Lefschetz number and Nielsen number. Mike Shulman and I have extended these results to the Reidemeister trace and eliminated many of the classical hypotheses. The key to our approach is to think of the Euler characteristic as an endomorphism rather than an integer. With this change in perspective, the product of integers becomes a composite of functions and the topological results follow from a more general (formal) theorem.

Thursday, February 21, 2013

2:00 pm   in 241 Altgeld Hall,  Thursday, February 21, 2013
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Submitted by collier3.
 Amelia Tebbe (UIUC Math)O-minimal Lefschetz Fixed Point TheoremAbstract: We can think of topological Euler characteristic as a special case of Lefschetz number. There is an o-minimal version of Euler Characteristic - can we think of it as a special case of some sort of o-minimal Lefschetz number? My goal for this talk is to gently lead up to Edmundo and Woerheide's o-minimal version of Lefschetz Fixed Point theorem, discussing the topological fixed point theorem and o-minimal Euler characteristic along the way.

Saturday, February 23, 2013

Midwest Topology Seminar
11:00 am   in 245 Altgeld Hall,  Saturday, February 23, 2013
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Submitted by franklan.
 Kathryn Lesh (Union College)Partition complexes, Bredon homology, and the Whitehead ConjectureAbstract: I'll discuss an adaptation of equivariant approximation techniques to the computation of Bredon homology. I'll apply it to compute the Bredon homology and cohomology of the partition complex with coefficients in a p-constrained Mackey functor (given some fine-print provisos on the $\Sigma_n$ action). There is a relationship to a proposed "non-computational" proof of the Whitehead Conjecture. This is joint work with Greg Arone and Bill Dwyer.

Midwest Topology Seminar
2:00 pm   in 245 Altgeld Hall,  Saturday, February 23, 2013
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Submitted by franklan.
 Nick Rozenblyum (Northwestern University)Higher trace maps and topological field theoriesAbstract: The Dennis trace map from the algebraic K-theory of a category to its Hochschild homology (and its numerous variants) is a fundamental object of study in geometry and topology. Hochschild homology of a category can be described as a kind of integral of the category over the circle, and this description provides a geometric construction of the trace map. I will describe a version of Hochschild homology given by integrating $(\infty,n)$-categories over higher dimensional manifolds called "composition cohomology", which provides the target for higher dimensional trace maps. From the point of view of manifold topology, this gives a universal construction of topological field theories. This is joint work with David Ayala.

Midwest Topology Seminar
3:30 pm   in 245 Altgeld Hall,  Saturday, February 23, 2013
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Submitted by franklan.
 Julianna Tymoczko (Smith College)Localization techniques in torus-equivariant cohomologyAbstract: Given a topological space X with a group action, the equivariant cohomology of X includes both the information from ordinary cohomology and the information of how the group acts on X. Though a priori more complicated than ordinary cohomology, equivariant cohomology is often easier to compute because of combinatorial techniques arising from the work of many, including Kirwan, Atiyah, Chang-Skjelbred, and especially Goresky-Kottwitz-MacPherson. We discuss this work and then show how to extend it beyond the circumstances in which it originally applied. This can be used to build a sort of Schubert calculus for a collection of varieties called Hessenberg varieties. We end with open questions.

Midwest Topology Seminar
5:00 pm   in 245 Altgeld Hall,  Saturday, February 23, 2013
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Submitted by franklan.
 Alejandro Adem (University of British Columbia)Topology of spaces of representations for abelian groupsAbstract: In this talk we describe recent work on the homotopy and equivariant K-theory with respect to conjugation for spaces of commuting elements in a compact Lie group. This is joint work with Fred Cohen and José Manuel Gómez.

Tuesday, February 26, 2013

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, February 26, 2013
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Submitted by franklan.
 Mona Merling (University of Chicago)Equivariant algebraic K-theoryAbstract: In the early 1980's, Dress and Kuku and Fiedorowicz, Hauschild and May introduced space level equivariant versions of the plus and Q constructions in algebraic K-theory. However, back then, the group action on the ring in question was taken to be trivial. We generalize these definitions to the case in which a finite group G acts nontrivially on a ring, an exact category, or a Waldhausen category, and we show how to construct a genuine equivariant K-theory spectrum from a G-ring. The main example of interest is that of a Galois extension. The equivariant constructions rely on finding categorical models for classifying spaces of equivariant bundles (a joint project with Guillou and May) and the use of equivariant infinite loop space machines such as the one developed by Guillou and May, or the equivariant version of Segal's machine. The comparison of these machines, which will allow their interchangeable use in algebraic K-theory constructions, is a joint project with May and Osorno. New ideas are needed since, among other things, the comparison theorem of May and Thomason fails equivariantly.

Thursday, February 28, 2013

2:00 pm   in 241 Altgeld Hall,  Thursday, February 28, 2013
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Submitted by collier3.
 Seckin Demirbas (UIUC Math)The Schodinger Equation on a compact 2 dimensional ManifoldAbstract: In this talk I will discuss local well posedness of the Schrondinger equation on a 2 dimensional compact manifold in Sobolev spaces. Throughout the talk I will develop the basic tools to prove local existence and sketch the proof of local well posedness.

Tuesday, March 5, 2013

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, March 5, 2013
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Submitted by rezk.
 Charles Rezk (UIUC Math)Orthogonal Spaces and Global Homotopy TheoryAbstract: "Global equivariant homotopy theory" is a setting which allows you to talk about equivariant homotopy theory for a whole family of groups (usually, all compact Lie groups) simultaneously. Stefan Schwede has a model for global stable equivariant homotopy theory, based on orthogonal spectra. He recently posted a preprint to his homepage on this, so now we can all learn about it. I'll give an expository talk about an unstable precursor of this: the "global" homotopy theory of orthogonal spaces.

Thursday, March 7, 2013

2:00 pm   in 241 Altgeld Hall,  Thursday, March 7, 2013
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Submitted by collier3.
 Grace Work (UIUC Math)Trajectories on Translation Surfaces Abstract: Studying the gaps in sequences has various applications in number theory, probability theory, and other mathematical areas. We will approach this topic from the perspective of geometry through the examination of the slopes of saddle connections on translation surfaces. We will begin with an overview of translation surfaces and saddle connections and then move to explore how the SL(2,R)-action on the moduli space of translation surfaces can help us understand the gap distributions for various sequences in [0,1).

Tuesday, March 12, 2013

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, March 12, 2013
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Submitted by franklan.
 Ryan Grady (Boston University)Factorization algebras and an application to algebraic index theoryAbstract: Factorization algebras are very general structures that encompass many algebraic notions, among them $E_n$ algebras, vertex algebras, and Hopf algebras. They have an intimate relationship with the homotopy sheaves of manifold calculus. I will introduce factorization algebras and some of their properties (e.g. factorization homology and descent) in a language developed by K. Costello and O. Gwilliam (themselves influenced by Beilinson, Drinfeld, and others). Factorization algebras appear from quantum field theory constructions as the algebra of observables. Using a particular quantum field theory, I will derive the algebraic index theorem. This talk is based on joint work with O. Gwilliam.

Thursday, March 14, 2013

Special Topology Seminar
11:00 am   in 243 Altgeld Hall,  Thursday, March 14, 2013
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Submitted by franklan.
 Erin Chambers (Saint Louis University)Topological measures of similarity on curvesAbstract: The question of how to measure similarity between curves in various settings has received much attention recently, motivated by applications in GIS data analysis, medical imaging, and computer graphics. While geometric measures such as the Hausdorff and Frechet distance have efficient algorithms, measures that take the underlying topology of the space are relatively new and unexplored. Several candidates have been proposed in recent years, but many of these are only tractable in restricted settings, and surprisingly little is known about their practicality. We will survey known results (both geometric and topological) in the first part of the talk, and then focus on new algorithmic results for the topological measures in the second half. The talk will conclude with open questions and possible new directions in this area.

2:00 pm   in 241 Altgeld Hall,  Thursday, March 14, 2013
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Submitted by collier3.
 Juan Villeta-Garcia (UIUC Math)Beginner Intersection Theory in Algebraic Geometry (part deux) Abstract: We continue last semester's talk on intersection theory in algebraic geometry. We begin with a quick review of last time, and delve into the definition of the chow group. We will give both an algebraic and geometric description. We will try to motivate the structure of the Chow ring. Finally, we end with a brief sketch of Chern classes of line bundles (mostly as a review for the speaker). As always, we will have lots of examples!

Tuesday, March 26, 2013

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, March 26, 2013
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Submitted by franklan.
 Yoshikata Kida (Kyoto University)Orbit equivalence rigidity for ergodic actions of mapping class groupsAbstract: I explain rigidity for ergodic free probability-measure-preserving (p.m.p.) actions of mapping class groups of surfaces. Namely, if any two such actions are orbit equivalent, then they are indeed conjugate. The idea of the proof is based on Ivanov's computation of the abstract commensurator of the mapping class group. Connection between these results is discussed. I also explain a superrigidity result on an action of the mapping class group, asserting that if it is orbit equivalent to an ergodic free p.m.p. action of an arbitrary group, then they are virtually conjugate.

Thursday, March 28, 2013

2:00 pm   in 241 Altgeld Hall,  Thursday, March 28, 2013
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Submitted by collier3.
 Bolor Turmukh (UIUC Math)Kac Moody Lie algebras and their representationsAbstract: We will start with a reminder about the definition of Lie algebras and some classic and important results about their representation. We will then generalize the definition of semi-simple Lie algebras and arrive at the definition of infinite dimensional Kac-Moody Lie algebras. We will discuss some attempts at classifying representations of Kac-Moody Lie algebras and hopefully concentrate on Affine Lie algebras.

Tuesday, April 2, 2013

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, April 2, 2013
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Submitted by franklan.
 Robion Kirby (UC Berkeley)Trisections of 4-manifoldsAbstract: Any smooth, orientable 4-manifold X has a trisection (analogous with Heegaard splittings in dimension 3) where each sector is diffeomorphic to a connected sum of k copies of $S^1 \times B^3$. These trisections are isomorphic up to stabilization, which is a connected sum with a simple trisection of $S^4$. Similar results hold when X has a boundary.

Thursday, April 4, 2013

2:00 pm   in 241 Altgeld Hall,  Thursday, April 4, 2013
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Submitted by collier3.
 Matej Penciak (UIUC Math)Enumerating Geometric Arrangements Abstract: Classical geometers were able to calculate the number of conics passing through four points and tangent to a fixed line. With "less work", we can use the cohomology of projective space to solve problems like this and to rederive Bezout's theorem. After introducing the Grassmannians and discussing their cohomology, we can go on to answer more complicated enumerative problems. Along the way, we will mention limitations to this approach, and if time permits, some of these limitations will be addressed.

Tuesday, April 9, 2013

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, April 9, 2013
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Submitted by franklan.
 John Klein (Wayne State University)Algebraic topology as applied to a problem in statistical mechanicsAbstract: An area of interest in statistical mechanics is the study of statistical distributions of stochastic currents generated in graphs. It turns out that this problem amounts to the study of loops of Markov processes that evolve according to the "master equation". Physicists have observed that, for almost every generated current, quantization occurs in the "adiabatic" and "low temperature" limits. My main goal in this talk will be to explain how this story can be understood using the standard tools of algebraic topology.

Thursday, April 11, 2013

2:00 pm   in 241 Altgeld Hall,  Thursday, April 11, 2013
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Submitted by collier3.
 Eliana Duarte (UIUC Math)Geometry of Points in the Projective PlaneAbstract: I will start by defining the Hilbert function and Hilbert polynomial for the homogeneous coordinate ring of a projective variety. Next, I will present some examples of how to compute the Hilbert function for a finite set of points in the projective plane. In particular I will explain how the Hilbert function gives geometric information about finite sets of points in the projective space.

Tuesday, April 16, 2013

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, April 16, 2013
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Submitted by franklan.
 Rolf Hoyer (University of Chicago)The Morava K-theory of finite groupsAbstract: We will consider the current state of knowledge and computation for the Morava K-theory of finite groups. This will start with classical results and their applications. As we move to more general cases, we will notice more and more holes in our algebraic understanding. In particular, we will focus on the issue of odd-dimensional elements, which exist for so-called "bad" groups.

Thursday, April 18, 2013

2:00 pm   in 241 Altgeld Hall,  Thursday, April 18, 2013
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Submitted by collier3.
 Nathan Fieldsteel (UIUC Math)An Introduction to Toric VarietiesAbstract: A toric variety is a complex variety $X$ containing a torus $(\mathbb{C}^{*})^n$ as an open subvariety so that the multiplicative action of the torus on itself extends to an action on $X$. Toric varieties appear in a diverse array of settings. We will give an introduction to the theory of toric varieties, with examples and classical constructions. Time permitting, we will touch on some open questions and connections to topology.

Tuesday, April 23, 2013

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, April 23, 2013
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Submitted by franklan.
 Moritz Groth (Radboud University Nijmegen)The additivity of traces in monoidal derivatorsAbstract: Peter May proved that in a category which is both triangulated and monoidal in a compatible way, the categorically defined Euler characteristic of dualizable objects is additive with respect to distinguished triangles. No pretense was made that this was a complete set of compatibility axioms, and, in fact, it was not sufficient to imply the additivity of more general traces. In this talk on joint work with Kate Ponto and Mike Shulman, we want to advertise stable, monoidal derivators as a framework for a formal study of the interaction of stability with monoidal structure. For such derivators the compatibility axioms of May are just various reformulations of naturality properties of "pushout products", and we are able to derive the more general additivity theorem at this level.

Thursday, April 25, 2013

2:00 pm   in 241 Altgeld Hall,  Thursday, April 25, 2013
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Submitted by collier3.
 Neha Gupta (UIUC Math)Subgroups of Small Cancellation GroupsAbstract: Small cancellation is a property for group presentations that has several geometric and algebraic applications. We will begin by defining various "versions" of small cancellation theory. We will try to understand how one can use it to conclude that certain subgroups of small cancellation groups are free. We will also talk about some (very) interesting open questions.

Tuesday, April 30, 2013

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, April 30, 2013
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Submitted by franklan.
 Ezra Getzler (Northwestern University)Lie infinity-categoriesAbstract: I explain how the definition of quasi-categories must be modified in the world of simplicial analytic spaces. (There are surprising similarities to the definition of complete Segal spaces.) I will also explain the main example: the nerve of a differential graded Banach algebra. This is joint work with Kai Behrend.

Thursday, May 2, 2013