# CUNY Graduate Center Topology Seminar

## General Information

The seminar meets Wednesdays 5:45-6:45 in room 4214.03 at the Graduate Center. The mathematics department lounge is room 4214.

The building is at 365 5th Avenue (34th St) in Manhattan.

Here are links for Parking lots in NY (the neighborhood is called Murray Hill).

## Schedule, Spring 2013

• Date Wed May 8 , 5:45- 6:45

• Speaker: Joey Hirsh/ CUNY, MIT

Title: Derived Noncommutative Deformation Theory

Abstract: We will explain the basic principles behind deformation theory, how deformation theory fits into homotopy theory, and how noncommutative deformation theory generalizes the classical commutative theory.

Restaurant: La Vie En Szechuan
14 E 33rd St.
Link to La Vie En Szechuan

NY Times review
Noodles about $10, chicken about$15.
We liked it so much we are going again.

• Date Wed April 10 , 5:45- 6:45

• Speaker: Jose La Luz. Hostos CC.

Title: THE HIGHER DERIVED FUNCTORS OF THE PRIMITIVE ELEMENT FUNCTOR OF QUASITORIC MANIFOLDS

Abstract: Quasitoric manifolds sit at the crossroads of topology and combinatorics. The clasification of these manifolds has been the focus of intense research among many researchers. The homotopy groups of quasitoric manifolds and other related toric spaces is an area of active research utilizing techniques across many discplined. The author will present results in a program to calculate the homotopy groups of these manifolds using machinery from homotopy theory, combinatorics and commutative algebra. The material to be presented generalizes previous results about the derived functors of coalgebras. In addition, another application regarding necessay conditions for ridigity of quasitoric manifolds will be discussed.

Restaurant: La Vie En Szechuan
14 E 33rd St.
Link to La Vie En Szechuan

NY Times review
Noodles about $10, chicken about$15.

• Date: Wed March 20, 5:45- 6:45

• Speaker: Jeremy Miller/ CUNY Graduate Center
Title: Localization and homological stability of configuration spaces

Abstract: Tom Church used representation stability to prove that the space of configurations of distinct unordered points in a closed manifold exhibit rational homological stability. In join work with Martin Bendersky, we give another proof using localization and rational homotopy theory. Our methods also yield new information about stability for torsion in the homology of configuration spaces of points in a closed manifold. For example, we prove that the 2 torsion in the group homology of spherical braid groups on an even number of strands stabilize while the 2 torsion in the group homology of torus braid groups on an odd number of strands stabilize.

Restaurant: Restaurant: \itemCopper Chimney
126 28th (between Lexington and Park Ave).
Indian Restaurant. Main courses between between $12 and$20.

• Date: Tuesday March 5, 6:45-7:45

• NOTE CHANGE OF DAY AND TIME.

Speaker Michael Barr/ McGill university

Title : Is every separated uniform space a limit of metric spaces.

Abstract. The answer is no. Following a conjecture of James Cooper, we have characterized limits of metric in terms of a weak completeness property. This characterization can be used to show that Omega, the first uncountable ordinal, with the uniform structure that it inherits from the compact space Omega+1, is not in the limit of metric spaces. This is a variation of the original example (epsilon_0) suggested by Cooper. This is joint work with John Kennison and Robert Raphael.

Restaurant: Bamiyan
358 3rd Ave
Between 26th and 27th
Afghan Restaurant.

• Date: Wed February 6. 5:45 - 6:45

• Speaker: John Klein/ Wayne State University
Title: Algebraic Topology as Applied to a Problem in Statistical Mechanics

Abstract: 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 probability distributions on the state space that evolve according to a certain "master equation." This master equation is a first order linear differential equation that is associated with a loop of Markov processes. 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.

Restaurant: Franchia - a Vegan, asian restaurant.

## Schedule, Fall 2012

• Date: Wed, Dec. 12th. 5:30-6:30

• Speaker: Sholom Rosen/ Retired!!
Title: Families of submodules of the mod 2 Steenrod Algebra and their realizations.
Restaurant:Szechuan-Gourmet
Link to Szechuan Gourmet web page

• Date: Wed Dec. 5, 5:30-6:30

• Speaker: Jeremy Miller/ CUNY Grad Center
Title: The topology of the space of J-holomorphic maps to CP^2
Abstract: In the 1970's, Graeme Segal proved that the space of holomorphic maps from a Riemann surface to a complex projective space is homology equivalent to the corresponding continuous mapping space through a range of dimensions increasing with degree. I will address if a similar result holds when other almost complex structures are put on projective space. For CP^2, I prove that the inclusion map from the space of J-holomorphic maps to the space of continuous maps induces a homology surjection through a range of dimension tending to infinity with degree. The proof involves comparing the scanning map of topological chiral homology (Salvatore, Lurie, Andrade) with gluing of J-holomorphic curves (Floer, McDuff-Salamon, Sikorav).
Restaurant: TBA

• Date: Tuesday, Nov. 20th, 5:15PM - 6:15PM
ROOM 3310 A
NOTE CHAGE OF DATE, TIME AND ROOM.

• Speaker: Tony Bahri/ Rider University
Title: On the topology of weighted projective spaces.

Abstract: As singular toric varieties, weighted projective spaces have an action of a real torus. The equivariant cohomology with respect to this action is isomorphic to the ring of piecewise polynomials on the defining fan. Choosing a particularly nice presentation of this ring allows the theory is to be seen as paralleling that for smooth toric varieties. The survey will include also a report on the complete topological classification of weighted projective spaces obtained in collaboration with Mattias Franz, Dietrich Notbohm and Nigel Ray.

Restaurant: TBA

• Date: Wed Nov. 14, 5:30-6:30

• Speaker: Tatyana Khodorovskiy/Hunter College
Title: Embeddings of Rational Homology Balls
Abstract: We will begin with a description of the rational homology balls appearing in Fintushel and Stern's rational blow-down procedure for smooth 4-manifolds, a generalization of the standard blow-down operation. We will then discuss various smooth and symplectic embedding results of these rational homology balls, as well as a description of a symplectic rational blow-up operation.

Restaurant:

• Date: Wed Oct.24, 5:30-6:30

• Speaker: Don Davis/Lehigh University
Title: Combinatorial number theory arising from algebraic topology.
Abstract: We will show how studying v1-periodic homotopy groups of SU(n) led to the following question. Let f(n) denote the sum of the reciprocals of the binomial coefficients (n choose i). For which p-adic integers x does the sequence f(x_n) approach a p-adic limit? Here x_n are the partial sums for x. The answer when p is odd is quite simple, but when p=2 is complicated and not completely understood.

Restaurant : Kang Suh. 1250 Broadway (32nd st).

• Date: Wed Oct. 3, 5:30-6:30

• Speaker: Rob Thompson/ CUNY Hunter College, Graduate Center

Title: Homotopy theory from the point of view of cohomology of profinite groups.
Restaurant: TBA

• Date: Wed Sept. 19, 5:30-6:30

• Speaker: Scott Wilson/ CUNY Queens College, Graduate Center
Title: Refined information in smooth compact families of unitary matrices

Abstract: This is joint work with T. Tradler and M. Zeinalian towards giving an elementary construction of (the odd part of) differential K-theory. The idea is to put an equivalence relation, finer than homotopy equivalence, on the set of maps of a manifold into the unitary group. We'll show that we obtain a group that fits nicely into commutative diagrams and exact sequences involving K-theory and differential forms.

Restaurant: \item Chimney
126 28th (between Lexington and Park Ave).
Indian Restaurant. Main courses between between $12 and$20.

## Schedule, Spring 2011

• Date: Wed April 27 5:30-6:30

• Speaker: Steven Simon / NYU
Title: Equivariant and Orthogonal Ham Sandwich Theorems
Abstract:
This talk will present two generalizations of the Ham Sandwich Theorem, which states that under very broad conditions, any n finite measures on R^n can be bisected by a single hyperplane. Giving the theorem a S^0 interpretation, we provide equivariant analogues for the finite subgroups of the spheres S^1 and S^3. Secondly, we ask for the maximum number of pairwise orthogonal hyperplanes which can bisect a generic set of m measures on R^n, m
Restaurant: TBA

• Wed April 13 5:30-6:30

• Speaker; Tilman Bauer/Vrije Universiteit- Amsterdam
Title: Formal plethories
Abstract:
The natural transformations between generalized multiplicative cohomology theories (on spaces) form the set of unstable operations for these cohomology theories. This set has a lot of structure: one can pointwise add and multiply operations, the diagonal gives a comultiplication, and one can compose operations. In my talk I will discuss an algebro-geometric setup for studying this kind of structure which is an extension of the concept of a formal group.
Restaurant: Ben's Kosher Deli - 209 W 38th Street

• Wed. Wed March 2 5:30-6:30

• SPEAKER: Matt Miller/ Vassar
TITLE: A brief history of k-equal arrangements
ABSTRACT : Since their appearance in the 1992 paper of Bjorner, Lovazs, and Yao on computational complexity theory, k-equal arrangements have been studied extensively, both for their combinatorial and topological properties. In this talk we describe the original motivation for studying k-equal arrangements and their continued role in the study of subspace arrangements. We focus on their relationship to the combinatorics of the partition lattice, some recursive formulas for the cohomology of their complements, and our recent results about Massey products and formality.
Restaurant: TBA

## Schedule, Fall 2010

• Wed. Dec 15 5:30-6:30

• SPEAKER: Mark Hovey/ Wesleyan University
TITLE: : Ideals in ring spectra
ABSTRACT: We present a rethinking of Jeff Smith's theory of ideals in ring spectra. The key point is that subobjects make no sense in homotopy theory, because every map is homotopic to an inclusion. So an ideal must be thought of as a map f rather than an object. This suggests study of the category of maps. This category turns out to have two different symmetric monoidal structures; in one such structure, a monoid is a homomorphism of ring spectra, but in the other, a monoid is precisely the definition Smith gave of an ideal of ring spectra. This work is still preliminary; in particular, calculations are sorely needed.
Restaurant: One of the vegetarian Indian restaurants on Lexington

• Wed Dec. 8 5:30-6:30

• SPEAKER: Shaun Ault/ Fordham University
TITLE: Elements Partially Annihilated by the Steenrod Algebra
ABSTRACT: We examine the dual of the so-called "hit problem", the latter being the problem of determining a minimal generating set for the cohomology of products of infinite projective spaces as module over the Steenrod Algebra (at the prime 2). The dual problem is to determine the set of $\mathcal {A}$-annihilated elements in homology. This set is easily shown to be a free associative algebra. Our current work shows that the set of elements that are annihilated by $Sq^i$ for each $i$ up to a fixed $2^k$ also forms a free associative algebra. Such a result could pave the way toward inductively determining all A-annihilateds.
RESTAURANT: TBA

• Wed December 1 5:30-6:30

• SPEAKER: Mark Behrens/MIT
TITLE: The homotopy groups of the K(2) local sphere at p > 3, revisited.
ABSTRACT: The stable homotopy groups of spheres admit a filtration called the chromatic filtration. The first layer of this filtration is completely understood. I will describe the structure of the second layer of this filtration, at primes > 3, building off of work of Shimomura and Yabe. <,br> Restaurant: TBA

• Wed Oct 20. 5:30-6:30

• ROOM 4214.03
SPEAKER: Don Davis/ Lehigh University
TITLE: Vector fields on the product of two real projective spaces.
ABSTRACT: The span of a manifold is the maximal number of linearly independent vector fields on it. Let P^n denote real projective space. We present current work on the question of whether span(P^m x P^n) exceeds span(P^m) + span (P^n).
RESTAURANT: TBA

## Schedule, Fall 2008

• Wed Nov 12 5:00-6:00

• Room: 4214
Speaker: Santiago Lopez de Medrano
Title: Moment-angle manifolds and intersection of quadrics

• Thursday Nov 20 (Note change of date)
TIME 3:30-4:30

• Room; TBA
Alex Suciu, Northeastern University
Title: Geometry and topology of cohomology jumping loci
Abstract: The cohomology jumping loci of a space X come in two basic flavors: the characteristic varieties (the support loci for homology with coefficients in rank 1 local systems), and the resonance varieties (the support loci for the homology of the cochain complexes arising from multiplication by degree 1 classes in the cohomology ring of X). I will discuss various ways in which the geometry of these varieties is related to the formality, (quasi-) projectivity, and homological finiteness properties of the fundamental group of X.
RESTAURANT: TBA

• Wed Dec 10; 5:00-6:00

• ROOM: 4214.03
Don Davis: Lehigh University
Title Immersions of real projective spaces.
Abstract: We review several recent results on the problem of finding the smallest Euclidean space in which RP^n can be immersed.
Restaurant: TBA

• Wed, Oct. 29
SPEAKER: Constance Leidy (Wesleyan University)
TITLE: The complexity of the structure of the knot concordance group

ABSTRACT: In 1997, T. Cochran, K. Orr, and P. Teichner defined a filtration of the classical knot concordance group. The filtration is defined in terms of gropes or Whitney towers and is connected to the classification of topological 4-manifolds. We will discuss some joint work with Tim Cochran and Shelly Harvey that establishes explicit families of knots that generate infinite rank subgroups of each filtration quotient.
Restaurant: Kung Shu

## Schedule, Spring 2008

• THURSDAY Apr. 10 5-6 PM (Note change of day).
Room: 4214-03 (Note change of room)
Tony Bahri/Rider University
Title: Piecewise Polynomials and the Equivariant Cohomology of Weighted Projective Spaces
Abstract: A report of joint work with Matthias Franz and Nigel Ray. Weighted projective spaces are the easiest examples of singular toric varieties. Unlike the case of smooth varieties, the integral equivariant cohomology ring depends on more than just the combinatorics of the underlying fan. We describe the ring structure in terms of piecewise polynomial functions on the fan. Unlike the ordinary integral cohomology, this ring distinguishes among weighted projective spaces.
Restaurant: TBA

• April 2 Laurentiu Maxim/Lehman college

TITLE: Atiyah-Meyer formulae for Hodge-type invariants of algebraic varieties.
ABSTRACT: I will report on recent progress on the study of genera and characteristic classes of algebraic varieties. I will describe Hodge-theoretic analogues of the Atiyah-Meyer signature formula, and discuss possible extensions of these results to the singular setting. This is joint work with S. Cappell, A. Libgober and J. Shaneson.
Restaurant: : Kang Suh. 1250 Broadway (32nd st).

• March 26 Nancy Hingston/College of New Jersey

Title: Loop products and closed geodesics
Abstract: The critical points of the energy function on the free loop space L(M) of a compact Riemannian manifold M are the closed geodesics on M. Filtration by the length function gives a link between the geometry of closed geodesics and the algebraic structure given by the Chas-Sullivan product on the homology of L(M). Geometry reveals the existence of a related product on the cohomology of L(M). For manifolds such as spheres and projective spaces for which there is a metric with all geodesics closed, the resulting homology and cohomology rings are nontrivial, and closely linked to the geometry. I will not assume any knowledge of the Chas-Sullivan product. Joint work with Mark Goresky.
Restaurant: TBA

• March 12 Joe Neisendorfer/University of Rochester

Restaurant: 2nd Avenue Deli
Title: Samelson products over loops on H-spaces

• Nov. 14 Bill Singer/Fordham University

Room: 6417
Restuarant: Kang Suh. 1250 Broadway (32nd st).
Title: "Rings of Symmetric Functions as Modules over the Steenrod Algebra".

## Schedule, Fall 2007

• Dec. 5 Don Davis/Lehigh University

Room: 6417
Restuarant: TBA
Title: From invariant theory to homotopy groups.
Abstract:
We determine the v1-periodic homotopy groups of all irreducible p-compact groups (BX,X). In the most difficult, modular, cases, we follow a direct path from their associated invariant polynomials to these homotopy groups. We show that, if p is odd, every irreducible p-compact group has X of the homotopy type of a product of explicit spaces related to p-completed Lie groups.

• Friday October 19, 10:00-11:00 am John Klein/ Wayne state University

Title: Bundle structures and Algebraic K-theory

Abstract:
This talk will describe algebraic K-theoretic obstructions to lifting fibrations to fiber bundles having compact smooth/topological manifold fibers. The surprise will be that a lift can often be found in the topological case. Examples will be given realizing the obstructions.

• Oct. 3 Jesus Gonzalez/ Centro de Investigacion, Mexico City

Title: Topological complexity of lens spaces
Abstract:
The topological complexity of lens spaces can be used to approach the immersion problem for odd dimensional projective spaces. Following work of Fadell-Husseini (1992) and Farber-Grant (2007), I will describe how to compute the initial stages in such an approach.

## Schedule, Fall 2006

• Oct. 25 Tony Bahri/ Rider University

Title: "Stable decompositions of complements of complex coordinate subspace arrangements and generalized moment angle complexes"

Abstract: A report of joint work with Martin Bendersky, Fred Cohen and Sam Gitler. We investigate a splitting, after one suspension, of a generalized moment angle complex into pieces related directly to the underlying simplicial complex defining it. In the particular case of the complements of complex coordinate subspace arrangements, our result implies a well known homology result of Goresky and MacPherson.
Restaurant: TBA

## Schedule, Spring 2006

• March 8 Joel Zablow

Title:On the relations and homology in the Dehn twist quandle of a surface

## Schedule, Fall 2005

• Nov 9, 1:30-2:30, Rm 8405Dennis Sullivan -Cuny Grad. Center

Title: Are the operations in the free loop space of a closed manifold invariants of homotopy type?

• Oct. 26 Hayden Harker,Vasser College

Title: Derived functors of the locally finite functor
Abstract: Define the functor G from A-modules to A-modules to be the locally finite functor where G(M) = {m in M | Am is finitely generated as a vector space}. We describe our interest in this functor and discuss the specific case when A is an exterior algebra over Z_2 with a countably infinite number of generators.

Restaurant:TBA

• Oct. 12Don Davis, Lehigh University

Title "Homotopy exponents of SU(n)."
Abstract: We use methods of combinatorial number theory to prove that some homotopy group of SU(n) has an element of order p^{n-1+[n/p^2]+[n/p^3]+...}
Restaurant: Ben's Deli 209 W 38th St. near 7th ave.

## Schedule, Spring 2005

• March 23 Selman Akbulut, IAS/MSU

Title: Topology and Geometry of G_2 manifolds.
Restaurant: TBA

• Feb. 16 Rob Schneiderman, NYU

Title: Whitney towers and low dimensional topology.
Restaurant: TBA
Abstract

## Schedule, Fall 2004

• Dec. 1 Martin Bendersky, CUNY Hunter College/Graduate Center

Title: A spectral sequence approach to normal forms.
Restaurant: Ben's Deli

• Nov. 17Craig Westerland, IAS

Title:Function Spaces from Surfaces and stable decompositions.
Abstract: We discuss the function spaces Map(X,M) of continuous maps from a surface, X, to a manifold M,,studying some multiplicative properties and giving a new stable splitting when M is a sphere.
Restaurant: TBA

• Oct. 27 Nancy Hingston, The College of New Jersey

Title: Subharmonic Solutions of Hamiltonian Equations on Tori
Abstract
Restaurant: TBA

## Schedule, Spring 2004

• March 17 Cindy Curtis, The College of New Jersey

Title: On the SL(2,C)-Casson Invariant.

• April 21 Stefan Bauer, IAS

Title: Refined Seiberg Witten Invariant
Restaurant: TBA

• April 28 John McCleary, Vassar College

Title: Contribution of Hinz Hopf
Restaurant: TBA

## Schedule, Fall 2003

• Oct. 15 Lee Mosher, Rutgers University, Newark

Title: Parageometric Automorphisms of Free Groups.

Abstract

• Oct. 29 Katarzyna Potocka, Lehigh University

Title: The number of summands in the v_1 periodic homotopy of SU(n)
Restaurant: Ben's Deli (38th St. and 7th Ave.)

• November 19Martin Bendersky, CUNY Hunter College/Grad Center

Title: Stable Geometric Dimension of Vector Bundles over RP^n
Restaurant: Crestanello (475 5th Ave. Between 40 and 41st)

## Schedul, Fall 2002

• Oct. 2 John Klein, Wayne State University

Title:Poincare Duality and Brave New Rings
Restaurant:TBA

## Schedule, Fall 2001

• Oct. 3 Martin Bendersky, Cuny Hunter College/Grad Center

Title: The K-Theory Bousfield Kan Spectral Sequence. Applications and Generalizations
Restaurant: TBA

• Oct. 17 Stephen Bigelow, University of Melbourne
Title: Homology and the Jones Polynomial
Abstract

• Oct. 24 Tom Shimkus, Lehigh University
Title: Immersing 2-torsion lens spaces
Abstract

• Nov. 7 Martin Arkowitz, Dartmouth College
Title: The Cone Length and Lusternik Schnirelmann Category of a Map
Restaurant:TBA

• Monday Nov. 12 4:00-5:00 PM, Room 9207 [Note change of day and room] Dev Sinha, Brown University
Title: The space of long knots
Abstract

Restaurant:TBA

• Dec. 5 Octav Cornea
Title: Lagrangian intersections and critical point theory

## Schedule, Spring 2001

• Feb. 7 Wojtek Chacholski, Yale University

Title: Cellular vs. Acyclic
Restaurant: Brew's, 34th st between lexigton and 3rd Ave. Very good burgers!
Abstract

• Feb. 21
Po Hu, IAS

Title: Duality for equivariant families of manifolds

• March 7
Chuck Weibel, Rutgers University

Title: Atiyah's real K-theory and algebraic K-theory of real varieties
Restaurant: Da Ciro (239 Lexinton Ave near 33rd St.)

• March 28
Bill Browder, Princeton University

Title: Homology decompositions and constructions of group actions.
Restaurant: Da Ciro

• April 18 Octav Cornea, University of Lille

Title: Hopf invariants and periodic orbits of Hamiltonian flows
Restaurant: TBA

• May 2 Zoltan Szabo, Princeton University

Title: Holomorphic disks and invariants for 3-manifolds and smooth 4-manifolds
Abstract: We will introduce and study topological invariants for closed 3 manifolds and smooth 4-manifolds. The 3-manifold constructions uses Heegaard diagrams and a version of Langrangian FLoer homology. The 4-manifold invariant uses the previous construction, a pairing on FLoer-homology and a handle decomposition of the 4 manifold. We will also present some applications in three and 4-manifold topology. This is a joint result with Peter Ozsvath.
Restaurant: TBA

• May 9 Noson Yonofsky, Brooklyn College

Title: A model category for algebraic 2-theories
Abstract
Restaurant: TBA

## Schedule, Fall 2000

• Sept 13.
Don Davis, Lehigh University

Nonimmersions of Real Projective Spaces Implied by eo_2
Restaurant: TBA

• Oct. 11 Leyla Batakci, Lehigh University

TItle: On the cohomology of the Steenrod Algebra mod nilpotence

• Oct. 18.
Joe Roitberg, CUNY/Hunter College

The product Formula for Lusternik-Schnirelmann Category
Restaurant: TBA

• Oct 25.
Bill Singer, Fordham University

Title: On the cohomology of Hopf algebra extensions
Restaurant:TBA (Bill does like Korean food)

• Nov. 1 Moira Chas, CUNY Graduate Center

Title: Lie Bialgebras of Closed Strings in Manifolds
Restaurant; TBA

• Nov. 15 Mike Fisher, Lehigh University

Title: A Proof of an exponent conjecture of Bousfield and related work.

• Dec 6 Ranja Roy, Union College

Title: The trace conjecture - A counterexample.
Abstract
Restaurant: TBA