The seminar meets Wednesdays 4:30-5:30 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 Wed. March 7, 4:30-5:30
Speaker: Steve Scheirer, Lehigh University **

**Title: "Topological complexity of graph configuration spaces," **

**Abstract: The topological complexity of a path-connected space X, denoted by TC(X), is an integer which can be thought of as the minimum number of "continuous rules" required to describe how to move between any two points of X. We will consider the case in which X is a space of configurations of n points on a graph. This space can be viewed as the space of configurations of n robots which move along a system of one-dimensional tracks. We will recall Farley and Sabalka's approach to studying these spaces using discrete Morse theory and discuss how this can be used to determine the topological complexity.
**

**Restaurant: 2nd Avenue Deli.
162 E 33rd Street, between Lexington and 3rd.
Link to 2nd Ave Deli
**

·
**Date Wed. February 28 4:30-5:30
Speaker: Robert Short, Lehigh University **

**Title: Relative Topological Complexity for Pairs of
Right-Angled Artin Groups **

**Abstract: Topological complexity is a homotopy invariant introduced by Michael
Farber in the early 2000s. Denoted TC(X), it counts the smallest size of
a continuous motion planning algorithm on X. In this sense, it solves optimally
the problem of continuous motion planning in a given topological
space. In topological robotics, a part of applied algebraic topology, several
variants of TC are studied. In a recent paper, I introduced the relative
topological complexity of a pair of spaces (X, Y ) where Y ⊂ X. Denoted
TC(X, Y ), this counts the smallest size of motion planning algorithms
that plan from X to Y .
Right-angled Artin groups have grown in importance lately with their
connection to braid groups and their connection to real-world robotics
problems. In this talk, we will present the background needed to compute
the relative topological complexity of pairs of right-angled Artin groups
and hopefully discuss the details of the optimal motion planner involved.
**

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

·
**Date Wed. December 6 4:30-5:30
Speaker: Joel Zablow **

**Title: Braid relations and deep braiding **

**Abstract: We'll look at deep braiding in groups, i.e. non-obvious braiding, ABA=BAB, among products of generators, looking first at deep braiding in symmetric groups among k-cycles in S_n, for k ≤ n. When n≤5 (and probably in general), there are graphs and polyhedra, which I call platihedra, which organize braided k-cycles and exhibit interactions between the algebra of braiding and the combinatorics of the polyhedra. Connected components of the graphs (or of platihedra) with braided k-cycle labeled vertices, exhibit quandle structures. We'll look at a criterion under which deep braids in S _n can be "lifted" to deep braids in the braid groups B_n. Time permitting, we'll see an extension of deep braiding to the mapping class group of a genus 2 surface (hinting at such in arbitrary genus), applications to forming deep commutation relations in a host of groups, and/or to analogs of the Zamolodchikov tetrahedron equation, relating surfaces in 4-space and 2-morphisms in certain braided monoidal 2-categories. **

**Restaurant:Vatan (a vegetarian Indian restaurant)
409 3rd Ave between 28th and 29th.
Link to Vatan. **

·
**Date Wed. Oct. 11, 5:00-6:00 NOTE CHANGE OF TIME
Speaker: Don Davis, Lehigh University **

**Title: n-dimensional Klein bottles**

**Abstract: An n-dimensional version of the Klein bottle arose in our work in topological robotics. We discuss how it arose, and various aspects of its algebraic and differential topology. **

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

·
**Date Wed. Sept. 27, 4:30-5:30
Speaker: Michael Harrison, Lehigh University **

**Title: The h-principle and totally convex immersions.**

**Abstract: The h-principle is a powerful tool in differential topology which is used to study spaces of functions with certain distinguished properties (immersions, submersions, k-mersions, embeddings, free maps, etc.). I will discuss some examples of the h-principle and give a neat proof of a special case of the Smale-Hirsch Theorem, using the "removal of singularities" h-principle technique due to Eliashberg and Gromov. Finally, I will define and discuss totally convex immersions and discuss some h-principle statements in this context. **

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

·
**Date Tuesday, January 31, 4:00 – 5:00 NOTE CHANGE OF DAY AND TIME.
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: **** Chennai Garden**** **

127 East 28th Street. Between Park and Lexington

Link
to Chennai Garden

·
**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 SPACE
Abstract 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 Lexington
Link 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 28th
A 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.**

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.**

**Speaker:
Mohamed Abouzaid, Columbia University **

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

**·
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 **

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

**·
Date: Wed. Feb 26, 5:00-6:00 **

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

**Speaker:
Luis Diogo, Columbia University **

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

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

**Speaker:
Sander Kupers, Stanford University **

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

**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**

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

**·
Date Wed May 8 , 5:45- 6:45
Speaker: Joey Hirsh/ CUNY, MIT **

**Title:
Derived Noncommutative Deformation Theory**

**·
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 **

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

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

**Restaurant:
Franchia - a Vegan, asian restaurant.
Link to Franchia **

**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**

**·
April 2 Laurentiu Maxim/Lehman college**

**·
March 26 Nancy Hingston/College of New Jersey**

**·
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**

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

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

**Title:
Bundle structures and Algebraic K-theory**

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

**·
Oct. 25 Tony Bahri/ Rider University**

**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**

**·
Oct. 12Don Davis, Lehigh University**

**·
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
**

**·
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**

**·
Oct. 27 Nancy Hingston, The College of New Jersey**

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

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

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

**Title: Refined Seiberg
Witten Invariant
Restaurant: TBA **

**· April 28 John McCleary,
Vassar College**

**Title: Contribution of Hinz
Hopf
Restaurant: TBA**

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

**Title: Parageometric
Automorphisms of Free Groups.
**

**· Oct. 29 Katarzyna Potocka,
Lehigh University **

**·
November 19Martin Bendersky, CUNY Hunter College/Grad Center**

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

**Title:Poincare
Duality and Brave New Rings
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__

**Feb. 21**

Po Hu, IAS

Title: Duality for equivariant families of manifolds

Restaurant: Kang Suh (1250 Broadway)**March 7**

Chuck Weibel, Rutgers University

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

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

**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