CUNY Graduate Center Topology Seminar

General Information

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).

another link for parking

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

Schedule, Spring 2020

Date Wed April 1, 4:30-5:30

Speaker: Inbar Klang, Columbia University

Title:The May-Milgram filtration and operadic cell structures

Abstract:This talk will begin with an overview of the May-Milgram filtration of iterated loop spaces, which uses a configuration space model for these spaces. I will then talk about operadic cell structures, and discuss joint work with Alexander Kupers and Jeremy Miller, in which we lift the May-Milgram filtration to an E_k-cellular filtration, where E_k is the little k-cubes operad.

Date Wed February 19, 4:30-5:30

Speaker: John Klein, Wayane State University

Title: Hypercurrents

Abstract:this talk poses the question as to what a higher dimensional analog of a continuous time Markov chain might be, in which the time parameter is replaced by arbitrary smooth manifold. As a partial answer, we introduce the notion of a "protocol," which consists of a space whose points are labeled by real numbers indexed by the set of cells of a fixed CW complex in prescribed degrees, where the labels are required to vary continuously. When the space is a one-dimensional manifold, then a protocol determines a continuous time Markov process. In the presence of a homological gap condition, we associate to each protocol a ‘characteristic’ cohomology class which we call the hypercurrent. The hypercurrent comes in two flavors: one algebraic topological and the other analytical. For generic protocols we show that the analytical hypercurrent tends to the topological hypercurrent in the 'low temperature' limit. We also exhibit examples of protocols having nontrivial hypercurrent.

Restaurant: Chennai Garden
127 E 28th St., between Park and Lexington Ave.
. .

Schedule, Fall 2019

Date Wed October 23, 4:30-5:30

Speaker: Gershom Bazerman

Title: Topological Aspects of Dependency Structures

Abstract: This talk will discuss Dependency Structures with Choice, a variant of the Event Structures used to give semantics to concurrent programming. Some basic results in order theory allow us to equip DSCs with the structure of a locale (i.e. an abstract topological space). This allows us to study dependency structures (and concurrent semantics, structures of knowledge representation, etc.) with topological tools. We will discuss how covering (i.e. "versioning") relations give rise to a localization-like monad with an associated logical interpretation and sketch a possible use of cohomology data in representing and calculating conflicts (i.e. mutual exclusions) in such structures.

Restaurant: TBA
. .

Date Wed September 25, 4:30-5:30

Speaker: Peter Patzt, Purdue University

Title: Tails of FI-modules

Abstract: Representation stability is a stability pattern for sequences of representations of families of groups such as symmetric groups or general linear groups. In the case of symmetric groups, this stability can be encoded using Church-Ellenberg-Farb's theory of FI-modules. While the rational behavior of representation stable sequences of symmetric group representations has been fairly well understood since the early days of the field, the integral behavior is much more mysterious. In this talk, I will present joint work with John Wiltshire-Gordon, in which we categorize the behavior of FI-modules over the integers in a stable range.

Restaurant: 2nd-Ave Deli.
162 East 33rd Street
. Link to 2nd Ave Deli .

Schedule, Spring 2019

Date Wed March 13, 4:30-5:30

Speaker: Ugur Yigit, University of Rocester

Title:RO(C2)-graded cohomology of C2-equivariant EilenbergMac Lane spaces

Abstract: In this talk, we calculate RO(C2)-graded cohomology of some C2-equivariant EilenbergMac Lane spaces as a module over the cohomology of a point. And then, we give the equivariant generalizations of the EHP sequence for G = C2, and time permitting, we give the C2-Lambda algebra, which are the systematic tools for computations of the homotopy groups of spheres in classical case.

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

Schedule, Fall 2018

Date Wed December 5, 4:30-5:30

Speaker: David Recio Mitter, Lehigh University

Title: Topological robotics and braid groups

Abstract: One of the main problems in robotics is that of motion planning. It consists of finding an algorithm which takes pairs of positions as an input and outputs a path between them. It is not always possible to find such an algorithm which depends continuously on the inputs. Studying this problem from a topological perspective, in 2003 Michael Farber introduced the topological complexity of a space, which measures the minimal (unavoidable) discontinuity of all motion planners on a given topological space. The topological complexity TC(X) turns out to be a homotopy invariant of the space X.

In this talk we will determine (or narrow down to a few values in some cases) the topological complexity of the unordered configuration spaces of aspherical surfaces (including surfaces with boundary and non-orientable surfaces). We will also see how this can be understood as the topological complexity of the surface braid groups.

This is joint work with Andrea Bianchi.

Restaurant: 2nd Ave. deli.

· Date Wed. Oct 10, 4:30-5:30

Speaker: Scott Wilson, Queens College

Title: A spectral sequence for almost complex manifolds

Abstract: I'll present a spectral sequence for almost complex
manifolds, converging to deRham cohomology, that generalizes the
Frolicher (bi-complex) spectral sequence of complex manifolds. The
differentials on various pages will be described and I'll explain how
the E_1 page can be identified with a natural generalization of
Dolbeault cohomology for almost complex manifolds. As applications,
I'll describe several explicit calculations for Lie groups and
nilmanifolds as a degeneration result for highly non-integrable almost
complex structures. This is recent joint work with Joana Cirici. A
preprint is available at arxiv:1809.01416

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

Schedule, Spring 2018

· Date Wed. April 18, 4:30-5:30
Speaker: Alina Vdovina, Hunter College

Title: "Low complexity algorithms in knot theory"

Abstract: We show that the genus problem for alternating knots with $n$ crossings, as well as the Seifert genus problem for an arbitrary knot, has time complexity $n\log (n)$ and is in Logspace$(n)$ and $TC^{0}$ complexity classes. Almost all alternating knots of given genus possess additional combinatorial structure, we call them standard. We show, that the equivalence problem for such knots with $n$ crossings also has time complexity $n\log (n)$ and is in Logspace$(n)$ and $TC^{0}$ complexity classes.

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

· Date Wed. April 25, 4:30-5:30
Speaker: Thomas Bartsch, Giessen University

Title: "A Mini-course on Detecting critical points with Borel cohomology"

Abstract: In this lecture I will show how Borel cohomology can be used to find critical points of functionals where classical topological tools like Lusternik-Schnirelmann category or the Krasnoselski genus are not sufficient

· Date Wed. April 18, 4:30-5:30
Speaker: Alina Vdovina, Hunter College

Title: "Low complexity algorithms in knot theory"

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

· 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

Schedule, Fall, 2017

· 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

Schedule, Spring, 2017

· 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

Schedule, Spring, 2016

· 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

Schedule, Fall 2015

· 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

Schedule, Spring 2015

· 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

Schedule, Fall 2014

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

Schedule, Spring 2014

· 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.

Date: Wed. April 30: 3:00-4:00 pm. Room 7395
NOTE CHANGE OF DAY, TIME AND ROOM!

Speaker: Sander Kupers, Stanford University

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: 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 28th
A 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.