The seminar meets Wednesdays 5:00-6:00 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).

For more information about the seminar, or to add a name to the seminar mailing list, contact Martin Bendersky

**Date Tuesday January 31, 4:15-5:15 (Note change of date and time). Room 3212.****Speaker: John Klein, Wayne State University**

**Title: ** **Applications
of higher dimensional spanning trees**.

**Abstract: **** ****I
will introduce the notion of a spanning tree in a finite CW complex **

**of
arbitrary dimension. We utilize this to give an analogue of
Kirchhoff's**

**electrical
and matrix-tree theorems in higher dimensions. **

**We
will also describe a new combinatorial invariant of a CW complex
called the **

**hypercurrent.
The latter is motivated by the investigation of stochastic motion of**

**cellular
cycles of a given dimension.**

**Restaurant: Restaurant:****
****Chennai
Garden ****127
East 28th Street. Between Park and Lexington****
**

**Date Wed. March 9, 5:00-6:00**

Speaker: Nick Kuhn, University of Virginia

**Title: The topological numerical polynomial ring**

**Abstract: Let P be the ring of polynomials over the rationals
that take integer values when evaluated on integers. This ring has
long been known to appear in algebraic topology as the K-homology of
infinite complex projective space. We have found P appearing in a
more basic way as the homology of a nice commutative ring spectrum we
are terming the topological numerical polynomial ring. **

**Restaurant: Restaurant: Kang Suh 1250 Broadway (near 32nd) **

**Date Wed. Feb 17, 5:00-6:00**

Speaker: Joe Neisendorfer, University of Rochester

**Title: THE BEST POSSIBLE BOUND ON THE EXPONENT OF THE HOMOTOPY
GROUPS OF AN ODD PRIMARY MOORE SPACE **

**Abstract: Let p be an odd prime. We shall prove that the
homotopy groups of a mod $p^r$ Moore space are annihilated by
$p^{r+1}$. The method is to apply a surprising general splitting
theorem and then a general "semi-splitting" theorem to the
loop space of a Moore space. Although this is an old result, the
proof has now been much improved and it can now be talked about. **

**Joe is willing to give a pre-talk if there is interest. Title
of Pre-talk: THE EXISTENCE OF HIGHER ORDER TORSION IN THE HOMOTOPY
GROUPS OF AN ODD PRIMARY MOORE SPACEAbstract of Pre-talk: Let p
be an odd prime. We shall prove the existence of infinite families of
torsion of order p^{r+1} in the unstable homotopy groups of mod $p^r$
Moore spaces. The method is to use the Bockstein spectral sequence to
study the representation of the differential graded Lie algebra of
mod $p$ homotopy into the mod $p$ homology of the loop space. **

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

**Date Wed. Dec 9, 5:00-6:00**

Speaker: Don Davis, Lehigh University

**Title: Topological Complexity of Spaces of Polygons.**

**Abstract: The topological complexity of a topological space X
is the number of rules required to specify how to move between any
two points of X. If X is the space of all configurations of a robot,
this can be interpreted as the number of rules required to program
the robot to move from any configuration to any other. A polygon in
the plane or in 3-space can be thought of as linked arms of a robot.
We compute the topological complexity of the space of polygons of
fixed side lengths. Our result is complete for polygons in 3-space,
and partial for polygons in the plane. **

**Carbone
Ristorante 331 W. 38th (between 8th and 9th) **

**Date Wed November 4, 5:00 - 6:00**

Speaker: Don Larson, Penn State, Altoona,

**Title: Modular forms and the beta family**

**Abstract: Let p be a prime greater than 3. In 2008, M. Behrens
proved the existence of a 1-1 correspondence between beta elements in
the p-primary Adams-Novikov spectral sequence and modular forms over
Z up to certain congruence conditions depending on p. The proof used
homotopical properties of a spectrum denoted Q. In this talk, I will
briefly highlight some previous work on the homotopy of Q at the
prime 3 (where Behrens' correspondence is not known to exist), and
then I will describe work in progress at higher primes that attempts
to make the correspondence explicit. The talk will be as expository
as possible. **

**Restaurant: TBA **

**Date: Wed, Sept 30, 5:00-6:00**

Speaker: Tony Bahri, Rider University

**Title: On the integral cohomology rings of toric orbifolds. **

**Abstract: A criterion is described which ensures that a toric
orbifold, determined by a simple polytope and a characteristic map,
has torsion free cohomology concentrated in even degree. The
description is shown to transform well under the simplicial wedge
construction. A report of joint work with Soumen Sarkar and Jongbaek
Song. **

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

**Date: Wed, April 22, 5:30-6:30**

Speaker: Doug Ravenel, University of Rochester

**Title: Inside the proof of the Kervaire invariant theorem or
How I got bitten by the equivariant bug. **

**DOUG AS AGREED TO GIVE AN INTRODUCTORY TALK BEFORE HIS LECTURE.
WE CANNOT GIVE A PRECISE TIME SINCE HE ARRIVES AT JFK AT 1 PM. MY
GUESS IS IT WILL START SOMEWHERE BETWEEN 2:30 AND 3.**

**Abstract: This talk will cover one aspect of the proof of the
Kervaire invariant theorem (proved with Hill and Hopkins), namely the
gap theorem. It says that \pi_{-2} of a certain spectrum \Omega
vanishes. It is the part of the paper that requires equivariant
methods not available before 2009. It turns out that once the
machinery has been set up, it follows from a surprisingly easy
calculation **

**Restaurant: Kang Suh 1250 Broadway (near 32nd) **

**Date: Wed, February 4, 5:30-6:30**

Speaker: John R. Klein, Wayne State University

**Title: Unlinked Embeddings and Functor Calculus **

**Abstract: This talk will be about the space of codimension zero
embeddings of a Poincare duality space in a disk. I will describe a
tower that interpolates from the space of "Poincare immersions"
to a certain space of "unlinked" Poincare embeddings. The
layers of this tower are described in terms of the coefficient
spectra of the identity appearing in Goodwillie's homotopy functor
calculus. Time permitting, I will relate these layers to the layers
of the tower that appear in the Goodwillie-Weiss manifold calculus. I
will also answer a question posed by Sylvain Cappell.**

**Restaurant: Chennai Garden 127 East 28th Street. Between
Park and LexingtonLink to
Chennai Garden **

**Speaker: Jeremy Miller, Stanford University**

**Date: Monday, Sept 29, 4:30-5:30**

Title: Representation stability for homotopy groups of configuration spaces

**Abstract: In the 1970s, McDuff proved that configuration spaces
of distinct unordered particles in an open manifold exhibit
homological stability. That is, H_i(Conf_k(M)) is independent of k
for k>>i. A natural follow up question is: Do the homotopy
groups also stabilize? From explicit calculations, one can show that
this is not the case. However, in joint work with Alexander Kupers, I
have shown that the rational homotopy groups of configuration spaces
of particles in simply connected manifolds of dimension at least 3
exhibit representation stability in the sense of Church and Farb.
This follows from a more general theorem we prove relating the
homotopy groups and cohomology groups of co-FI-spaces and from the
work of Church on representation stability for the cohomology of
ordered configuration spaces. This result on homotopy groups suggests
that in situations with homological stability, one should not expect
classical stability for homotopy groups. Instead, one should try to
incorporate the fundamental group into the definition of stability. **

**Restaurant: Pippali, 129 E 27th St Link
for Yelp reviews: **

**Date: TUESDAY OCTOBER 7, 4:00-5:00**

NOTE CHANGE OF DAY AND TIME!

**Speaker: Don Davis, Lehigh University Title: On the
topological complexity of 2-torsion lens spaces**

**Abstract: The topological complexity of a topological space is
the minimum number of rules required to specify how to move between
any two points of the space. A ``rule'' must satisfy the requirement
that the path varies continuously with the choice of end points. We
use connective complex K-theory to obtain new lower bounds for the
topological complexity of 2-torsion lens spaces. We follow a program
set up by Jesus Gonzalez, and answer a question posed by him. **

**Restaurant: Mandoo Bar 2 W. 32nd Street, between Broadway
and 5th Yelp
review **

**Date: Wed October 15, 5:00-6:00**

**Speaker: Joana Cirici **

**Title: Topology of complex projective varieties with isolated
singularities**

**Abstract: I will explain a homotopical treatment of
intersection cohomology recently developed by
Chataur-Saralegui-Tanre, which associates a "perverse homotopy
type" to every singular space. In this context, there is a
notion of "intersection-formality", measuring the vanishing
of Massey products in intersection cohomology. The perverse homotopy
type of a complex projective variety with isolated singularities can
be computed from the morphism of differential graded algebras induced
by the inclusion of the link of the singularity into the regular part
of the variety. I will show how, in this case, mixed Hodge theory
allows us prove some intersection-formality results (work in progress
with David Chataur).**

**Restaurant: Dhaba Link
to Dhaba 108 Lexington Ave (between 27th St & 28th St)
New York, NY 10016 **

**Date: Wed October 22, 5:00-6:00**

**Speaker: John Mccleary, Vassar College **

**Title: Loop space homology, string homology, and closed
geodesics**

**Abstract: The homology of free loop space of a manifold enjoys
additional structure first identified by Chas and Sullivan. The
string multiplication has been studied by Ralph Cohen and John Jones
and together with J.~Yan, they have introduced a spectral sequence
converging to string homology that is related to the Serre spectral
sequence for the free loop space. Using this tool, and the work of
Felix, Halperin, Lemaire and Thomas, Jones and I establish some
conditions on manifolds that guarantee the existence of infinitely
many closed geodesics on the manifold in any Riemannian metric.
Restaurant: Lalibela Ethiopian Restaurant 37 E 29th St (Between
madison and Park)Lalibela
**

**Date: Wed. May 14, 5:00-6:00**

**Speaker: Inna Zakharevich, Institute for Advanced Study**

**Title: Scissors congruence and algebraic K-theory**

**Abstract: Hilbert's third problem asks the following question:
given two polyhedra with the same volume, can we decompose them into
finitely many pairwise congruence pieces? The answer, provided by
Dehn in 1901 is no; there is a second invariant on polyhedra, now
called the Dehn invariant. Classical scissors congruence asks this
question in other dimensions and geometries. In this talk we
construct an abstract framework for discussing scissors congruence
problems using algebraic K-theory. By discarding much of the
geometric underpinning of scissors congruence problems we are able to
construct decomposition invariants in much more general settings,
including Grothendieck rings of arbitrary models. As an application
of this framework we construct a "derived Grothendieck ring of
varieties".**

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

**Date: Wed May 7, 5:00-6:00**

**Speaker: Rob Thompson, Hunter College/ CUNY Grad Center**

**Title: An unstable Morava change of rings theorem for
Lubin-Tate homology**

**Abstract: The Morava Change of rings theorem is a central
result in stable homotopy theory. For certain spectra it allows one
to compute the E_2-term of the Adams-Novikov Spectral Sequence (i.e.
the Adams spectral based on complex cobordism) in terms of the
E_2-term of the Adams spectral based on various periodic homology
theories like Johnson-Wilson theory (a generalization of topological
K-theory), Morava K-theory ( a generalization of mod p K-theory), and
Lubin-Tate theory (a homology theory based on the theory of lifts of
the Honda formal group law to complete local rings whose residue
fields are F_p algebras). A number of results along these lines in
the unstable realm have been obtained. In this talk I will focus on
the case mentioned in the title. **

**Restaurant: Restaurant: Kokum, 106
Lexinton Ave, between 27th and 28thA south Indian vegitarian
restaurant. Here is the link. Kokum
**

**Date: Wed Apr. 30, 5:00-6:00**

**Speaker: Rita Jimenez Rollan, Northeastern University**

**Title: The cohomology of M_{g,n} and other representation
stability phenomena **

**Abstract: Let M_{g,n} be the moduli space of genus g Riemann
surfaces with n marked points. Given a non negative integer i, we
want to understand how the i-th rational cohomology group of M_{g,n}
changes as the parameter n increases. It turns out that the symmetric
group S_n acts on it and the sequence of S_n-representations
``stabilizes'' in a certain sense once n is large enough. In this
talk I will explain the behavior of this and other examples via the
language of representation stability. Moreover, I will introduce the
notion of a finitely generated FI-module and show our sequence of
interest has this underlying structure which explains the stability
phenomena mentioned above. As a consequence we obtain that, for n
large enough with respect to i, the i-th Betti number of M_{g,n} is a
polynomial in n of degree at most 2i. **

**Restaurant: Hunan Manor. 339 Lexington Ave (at 39th
St.)Link
to NY Times review. **

**Date: Wed. April 30: 3:00-4:00 pm. Room 7395**

NOTE CHANGE OF DAY, TIME AND ROOM!

**Speaker: Speaker: Sander Kupers, Stanford University**

**Title: E_n-cell attachments and a local to global homological
stability theorem.**

**Abstract: We define degreewise bounded generation for framed
E_n-algebras in chain complexes and prove that this property is
equivalent to homological stability. Using this we prove a
local-to-global principle for homological stability, in the sense
that if a framed E_n-algebra A has homological stability (or
equivalently the topological chiral homology of R^n with coefficients
in A has homology stability), then so has the topological chiral
homology of any open oriented connected manifold M with coefficients
in A. **

**Date: Wed. Apr 2, 5:00-6:00**

**Speaker: Mohamed Abouzaid, Columbia University **

**Title: Title: Lagrangian immersions and the Floer homotopy type
**

**Abstract: A conjecture of Arnold would imply that every exact
Lagrangian in a cotangent bundle is isotopic to the zero section
through Lagrangian embeddings. We now know that every such Lagrangian
is homotopy equivalent to the zero section. I will explain how,
combining the h-principle with the spectrum-valued invariants
introduced by T. Kragh, one can hope to show that such Lagrangians
are in fact isotopic to the zero section through Lagrangian
immersions. I will discuss partial results obtained with Kragh,
constraining the Lagrangian isotopy class of Lagrangians embeddings.**

**Restaurant: Kokum, 106 Lexinton Ave, between 27th and 28thA
south Indian vegitarian restaurant. Here is the link. Kokum
**

**Date: Wed March 26, 5:00-6:00**

**Speaker: Kate Poirier/ CUNY City Tech**

**Title: On the higher topological Hochschild homology of F_p and
commutative F_p-group algebras **

**Abstract: The construction of the classical Hochschild homology
of an algebra uses a simplicial model for the circle. Higher
Hochschild homology uses higher-dimensional spheres. The
constructions of topological Hochschild and higher topological
Hochschild homology model the algebraic constructions and replace
algebras by spectra. In his thesis, Torleif Veen calculated higher
Hochschild and higher topological Hochshild homology for finite
fields F_p, assuming certain bounds. In this talk, we review the
definitions and Veen's results and show how his bounds may be pushed
and his calculations generalized.**

**Restaurant: :Lalibela Ethiopian Restaurant 37 E 29th St
(Between madison and Park)Lalibela
**

**Date: Wed. Feb 26, 5:00-6:00**

**Speaker: Mahmoud Zeinalian **

**Title: A concise construction of differential K-theory **

**Abstract:One knows a generalized cohomology theory h tensor
the reals is canonically isomorphic to ordinary cohomology with
coefficients in h[point] tensor the reals. Representing the latter by
deRham forms and the former by classes of objects like maps into a
universal space one can form triples consisting of a pair of these
objects and an equivalence between their real images represent
elements in a formal fibre product as in homotopy theory. Equivalence
classes of these triples define a functor that combines differential
forms and the cohomology theory h called differential cohomology with
flavor h.The first one appeared in the 70s [the foliation decade] and
was a natural receptacle for the chern simons invariant and other
secondary invariants related to bundles with connections or to
foliations. There has been interest recently in axiomatizing
differential cohomology in general and to give more geometric models
for particular theories. There are two axioms that hold for and
characterize many specific examples. They involve a diagram building
on the fibre product idea [introduced in the chern simons example]
and an integration along the fibres of the product bundle with fibre
the circle introduced more recently. The second axiom replaces the
suspension axiom of usual cohomology theories. For differential
theories with flavor complex Ktheory the situation of geometric
models and axioms that characterize is known and satisfactory in the
even degree but heretofore unknown in the odd degree. In this lecture
we will build a new geometric model of differential K theory in both
degrees, eliminating one part of the triple and introducing a
geometric spectrum, and verify both the diagram and the the
integration along circle fibres axiom. Thus it will follow from known
work that any differential theory with flavor complex K-theory
satisfying the diagram and the integration along the circle fibres
axiom will be naturally isomorphic to our constructed
theory.Restaurant: TBA **

**Date: Wed. Dec 4, 5:00-6:00**

**Speaker: Luis Diogo, Columbia University **

**Title: Symplectic homology from Gromov-Witten theory **

**Abstract Symplectic homology is a very useful tool in the
study of symplectic manifolds. I will review the construction of this
invariant and its deep relations with string topology. Despite its
usefulness, symplectic homology can be very hard to compute
explicitly. I will talk about joint work with Sam Lisi, on a
procedure to compute this invariant for a class of symplectic
manifolds. This method uses information about holomorphic spheres on
symplectic manifolds, which can sometimes be obtained using tools
from algebraic geometry. Restaurant: Hunan Manor. 339
Lexington Ave (at 39th St.)Link
to NY Times review. **

**Date: Wed. October 23, 5:00-6:00**

**Speaker: Sander Kupers, Stanford University **

**Title: Topological chiral homology and homological stability
for completions**

**AbstractAn interesting phenomenon is that the configuration
space of particles on an open manifold has homology independent of
the number of particles in an increasing range. Such configuration
spaces are one of the simplest examples of topological chiral
homology, which is a homology theory for n-dimensional manifolds
taking values in spaces and taking E_n-algebras as coefficients. I
will explain how many previous results on homological stability,
including that for configuration spaces, fit into the framework of
topological chiral homology and are a consequence of a general result
by myself and Jeremy Miller.**

**Restaurant: Dhaba Link
to Dhaba 108 Lexington Ave (between 27th St & 28th St)
New York, NY 10016 **

**Date: Wed, October 9, 5:00-6:00**

Speaker: Joana Cirici

**Title. Rational homotopy of singular complex varieties**

**Abstract. The rational homotopy type of a singular complex
variety can be read from the first term of a spectral sequence
encoding cohomology groups of smooth projective varieties. This
result is based on Deligne's theory of mixed Hodge structures, and
generalizes the Formality Theorem of compact Kahler manifolds. I will
show how to compute this spectral sequence in simple examples and
provide some applications to the topology of singular complex
varieties.**

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

**Date: Wed October 2, 5:00-6:00**

Speaker: Pavle Blagojevic, Freie University, Berlin/Mathematical Institute SASA, Belgrade

**Title: "On k-regular maps"**

**Abstract: The question about the existence of a continuous
k-regular map from a topological space X to an N-dimensional
Euclidean space R^N, which would map any k distinct points in X to
linearly independent vectors in R^N, was first considered by Borsuk
in 1957. In this talk we present a proof of the following theorem,
which extends results by Cohen--Handel 1978 (for d=2) and Chisholm
1979 (for d power of 2): For integers k and d greater then zero,
there is no k-regular map R^d -> R^N for N < d(k-a(k))+a(k),
where a(k) is the number of ones in the dyadic expansion of k. Joint
work with G. M. Ziegler and W. Luck. **

**Restaurant: TBA **

**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.Link
to Copper Chimney **

**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: Bamiyan358 3rd
AveBetween 26th and 27th Afghan Restaurant.Link
to Bamiyan **

**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. Link
to Franchia **

**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. **

**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

**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

**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**

**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 geodesicsAbstract: 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 DeliTitle: Samelson products over
loops on H-spaces**

**Nov. 14 Bill Singer/Fordham University**

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

**Dec. 5 Don Davis/Lehigh University**

**Room: 6417Restuarant: TBATitle: 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 spacesAbstract: 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.**

**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 **

**March 8 Joel Zablow**

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

**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 functorAbstract:
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. **

**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 **

**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
ToriAbstract Restaurant: TBA**

**March 17 Cindy Curtis, The College of New Jersey**

**Title: On the SL(2,C)-Casson Invariant. Restaurant: Kang
Suh (1250 Broadway) **

**April 21 Stefan Bauer, IAS**

**Title: Refined Seiberg Witten InvariantRestaurant: TBA **

**April 28 John McCleary, Vassar College**

**Title: Contribution of Hinz HopfRestaurant: TBA**

**Oct. 15 Lee Mosher, Rutgers University, Newark**

**Title: Parageometric Automorphisms of Free
Groups.AbstractRestaurant:Kang Suh
(1250 broadway) **

**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) **

**Oct. 2 John Klein, Wayne State University**

**Title:Poincare Duality and Brave New RingsRestaurant:TBA **

**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

**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

Restaurant: Kang Suh (1250 Broadway)**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**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

CUNY/ Graduate Center

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

**Schedule, Fall 2000**

**Return to the Grad Center Math Department.**