Presentations at 9:30am on Saturday
Name: Belk, Marissa
University: Cornell University
Email: mathbat@gmail.com
Title: Finding Homologies of Sphere Quotients
Abstract: We will discuss quotients of spheres by linear, effective actions of elementary abelian groups, finite cyclic groups,
and tori. Using some basic representation theory, we will associate a matroid to many of these actions. We will then explore
the connections between the Poincare polynomial of a quotient and the Tutte polynomial of its associated matroid.
Room Number: S2 140
Name: Fein, Gregory
University: Rutgers University-Newark
Email: gmfein@rutgers.edu
Title: A tree grows in Binghamton, (and a group acts upon it.)
Abstract: In this talk, I’ll take you on a brief tour of some structure theorems for groups having actions on trees. Well
start with Bass and Serre and their simplicial trees and continue through Rips Theory for R-trees. If there’s time, I’ll also
mention a bit about group actions on the next natural generalizations: Λ- trees for Λ any ordered abelian group.
Room Number: S2 145
Name: Wilcox, Elizabeth
University: Binghamton University
Email: wilcox@math.binghamton.edu
Title: Wreath Product Unraveled
Abstract: This talk will de-mystify wreath products, with a clear and concise definition and pretty examples. Classic
applications and some of the usual subgroups (for example, the center) will be discussed. Additionally, a discussion of automorphisms of wreath products and complete groups will compose the latter part of the talk.
Room Number: SL 206
Name: Lodha, Yash
University: Cornell University
Email: y1763@cornell.edu
Title: An interesting consequence of a purely topological statement in the event of the failure of the continuum hypothesis.
Abstract In the event of the failure of the continuum hypothesis, lots of interesting questions can be asked. The positive
answer to some of these questions can be amalgamated into a single axiom called Martin’s axiom. This axiom is equivalent
to a purely topological statement. In this talk my goal is to prove that for a cardinal k that lies strictly between cardinals ω
and 2ω , it follows from Martin’s axiom that 2k = 2ω .
Room Number: SL 210
Presentations at 10:10am on Saturday
Name: Brazas, Jeremy
University: University of New Hampshire
Email: jtv5@unh.edu
Title: The Topological Fundamental Group and Hoop Earring Spaces
Abstract: The idea of endowing the fundamental group with a topology is not new. It has been used to generalize the
classification theorem of covering spaces to spaces lacking universal covers and the resulting functor, π1top , has been shown
to be a finer invariant than the mere fundamental group. Yet, the many claims in the literature that π1top is a functor to
the category of topological groups has just been recently shown, independently by Andrew Fabel and the author, to be
false. In this talk, we describe the topological fundamental group as a functor from the category of based topological spaces
to the category of quasi-topological groups. We then discusss how to compute π1top on hoop earring spaces (ΣX+ , x) of
totally path-disconnected, Hausdorff spaces X via a factorization of the identifying quotient map Ω(ΣX+ , x) → π1top (ΣX+ , x)
through a free topological monoid with involution. An embedding X → π1top (ΣX+ , x) illustrates that when X is not regular,
π1top (ΣX+ , x) is not a topological group. We’ll finish with a brief discussion of some open questions motivated by this new
development.
Room Number: S2 140
1
Name: Jones, Keith
University: Binghamton University
Email: kjones@math.binghamton.edu
Title: Controlled Connectivity and Tree Actions
ρ
Abstract: Given a finitely generated group G, controlled connectivity uses an action G ! M by isometries on a proper
CAT(0) space to ask about “connectivity of G with respect direction”, where the directions are given by ∂∞ M (the boundary
at infinity of M). The invariant Σ1 (ρ) records the set of directions in which G is controlled connected through ρ. This is a
generalization of the Bieri-Neumann-Strebel invariant Σ1 (G), which (along with its higher dimensional analogs) has found
many applications in determining topological finiteness properties of groups. This talk is about recent work calculating the
invariant for a family of actions in the case where ρ is cocompact and M = T is a simplicial tree. I will briefly review
the necessary notions on CAT(0) spaces, introduce the invariant Σ1 (ρ) (along with some interesting examples), and finally
discuss the application of Covering Spaces and Bass-Serre theory to obtain results on Σ1 for tree actions.
Room Number: S2 145
Name: Feldman, Arnold
University: Franklin & Marshall College
Email: afeldman@fandm.edu
Title: What is a tF -group?
Abstract: A t-group is a group in which each subnormal subgroup is normal, i.e., a group in which normality is transitive.
The purpose of the first part of this talk is to describe a certain class of formations of finite solvable groups and explain what
F-subnormality means for a formation F in this class. (For the special case that the formation is N , the formation of finite
nilpotent groups, N -subnormality is just subnormality.) F-subnormality, like subnormality, is transitive, leading to a natural
definition of a tF -group: a group in which each F-subnormal subgroup is normal. (Hence a tN -group is just a t-group.) The
second part of the talk will include examples of tF -groups for some choices of F, revealing that many, but fortunately not
all, choices of F lead to identical definitions of tF -group.
Room Number: SL 206
Name: Thomas, Viji
University: Binghamton University
Email: vthomas@math.binghamton.edu
Title: Free products and the box-tensor product of groups: a commutator connection
Abstract R. Brown and J.-L. Loday introduced the nonabelian tensor product of groups in connection with homotopy
theory. The box-tensor product is a generalization of the nonabelian tensor product. N.R.Rocco, G.J.Ellis and F.Leonard
introduced a construction related to the nonabelian tensor product of groups. In this talk I will give a generalization of this
construction for the box-tensor product of groups and provide some examples.
Room Number: SL 210
Presentations at 11:00am on Saturday
Name: Samuel, Matthew
University: Rutgers University
Email: matthematics@gmail.com
Title: Equivariant Cohomology of Isotropic Grassmannians
Abstract: An isotropic Grassmannian is a space of planes that are isotropic with respect to a bilinear form. The Lagrangian
Grassmannian (type C) and the odd and even orthogonal Grassmannians (types B and D) are examples of maximal isotropic
Grassmannians, consisting of such planes of maximal dimension. We and others have found relatively simple formulas for
Schubert classes in the equivariant cohomology of maximal isotropic Grassmannians (over the complex numbers). To our
knowledge, no one has yet found such a formula for submaximal isotropic Grassmannians. By analogy with our previous
work, we have surmounted what we believe is one of the primary difficulties in the submaximal case in types B and C. We
will discuss the story of equivariant cohomology of flag varieties, our recent accomplishment, and how we intend to leverage
it into a tableau formula.
Room Number: S2 140
2
Name: Finegold, Brie
University: University of California at Santa Barbara
Email: briefly@math.ucsb.edu
Title: A simplicial complex on which SL(n,R) acts nicely
Abstract: When a group acts co-compactly on a simply connected CW complex,one can recover a presentation (generators
and relations) for the group in terms of stabilizers of cells. Given any commutative ring R with one, consider SL(n,R), the
group of nxn matrices with entries from R and determinant one. I will define the nth Torus Complex over R, a complex on
which SL(n,R) acts simplicially. For certain rings R and certain n, the nth Torus Complex over R is path connected and
simply connected, and we can calculate a presentation using the theory of complexes of groups. In particular, we derive a
new palindromic presentation of SL(3,Z).
Room Number: S2 145
Name: Guzman, Fernando
University: Binghamton University
Email: fer@math.binghamton.edu
Title: Natural Duality for Boolean Semirings
Abstract: Joint work with Daniel Clouse, a former graduate student at Binghamton.
The variety of Boolean semirings, which is generated by a 3-element semiring S, is dual to the category of partially Stone
spaces. In this work, we place that well-known duality in the context of natural dualities, and construct a topological structure
S
that yields an optimal natural duality between the quasi-variety generated by S and the corresponding category generated
!
by S.
A poset description of some of the partially Stone spaces, “hairy cubes”, will be presented.
!
Room Number: SL 206
Name: Price, Candice
University: University of Iowa
Email: cprice@math.uiowa.edu
Title: A discussion on the combinatorial version of knot Floer Homology.
Abstract In 2000 Peter Ozsváth and Zoltán Szabó developed an invariant for closed oriented 3-manifolds called Heegaard
Floer homology. In 2002/3, they and independently Jacob Rasmussen, extended this invariant to knots in S 3 . This new
"
theory, knot Floer homology associates an abelian group HF
K(K) to a knot K. While the generators of the chain complex
were defined combinatorially, the differentials were defined analytically using holomorphic discs. In 2007, Osváth along with
Ciprian Manolescu and Sucharit Sarkar published a paper that gave a full combinatorial description of knot Floer Homology.
The goal of this presentation is to briefly describe this combinatorial version and to compute an example.
Room Number: SL 210
Presentations at 11:40am on Saturday
Name: Puri, Karan
University: Queensborough Community College - CUNY
Email: kpuri@qcc.cuny.edu
Title: Half-Turns in Hyperbolic Space
Abstract: Half-turns in hyperbolic 3-space H3 are orientation preserving involutions that fix a hyperbolic line pointwise.
Moreover, any orientation preserving isometry of H3 may be written as the product of two such half-turns. We generalize
this definition of half-turns to hyperbolic n- space, Hn and discuss the factorization of isometries of H4 as products of halfturns in some more detail.
Room Number: S2 140
Name: Sabalka, Lucas
University: Binghamton University
Email: sabalka@math.binghamton.edu
Title: Out(Fn )
Abstract: The group of outer automorphisms of a free group is a rich and complicated group. The topology and algebraic
invariants of this group are fairly well understood, but there is still much to understand about the geometry. In this expository
talk, we will go through the relevant definitions and important theorems. We will end with some suggestions about future
directions of research related to the geometry of Out(Fn ).
Room Number: S2 145
3
Name: Ganev, Iordan
University: Miami Univeristy of Ohio
Email: ganeviv@muohio.edu
Title: Groups of Square-Free Order
Abstract: One of the first advances in the enumeration of finite groups is Hlder’s formula for groups of a square-free order.
The aim of the project and presentation is to elucidate this classical result through a structural approach. In the process,
we introduce concepts such as nilpotency, the Fitting subgroup, the transfer homomorphism, and extensions. There is little
hope that Hlder’s formula generalizes to (k+1)-free integers; a more promising direction is to study the asymptotic behavior
of the group number function on such integers. We also discuss Higman’s PORC conjecture.
Room Number: SL 206
Name: Hodos, Rachel
Institution: NASA
Email: rachel.hodos@jpl.nasa.gov
Title: Using Topology to find voids in the Galactic Distribution
Abstract The recent development of homology algorithms (counting holes) in computational algebraic topology is providing
new tools for data analysis. We explore applications of these ideas to finding large-scale structure in the galactic distribution.
Room Number: SL 210
Presentations at 2:40pm on Saturday
Name: Kinlaw, Paul
University: Dartmouth College
Email: Paul.Kinlaw@dartmouth.edu
Title: Topology of Y x -Riemannian Manifolds
Abstract: A complete Riemannian manifold (M, g) is called a Ylx - manifold if every geodesic γ parametrized by arc length
with γ(0) = x satisfies γ(l) = x for some l "= 0. Bérard and Bergery proved that a Ylx -manifold of dimension > 1 is compact
and has finite fundamental group. We call (M, g) a Y x -manifold if for every & > 0 there exists l with |l| > & such that for
every geodesic γ parametrized by arc length with γ(0) = x, we have d(γ(l), x) < &. We will cover recent work, including
a proof that Y x -manifolds of dimension > 1 are compact with finite fundamental group. We will discuss the relationship
between Ylx and Y x -manifolds and refocusing Lorentz manifolds.
Room Number: S2 140
Name: Rueckriemen, Ralf
University: Dartmouth College
Email: ralf.rueckriemen@dartmouth.edu
Title: The spectrum of a quantum graph
Abstract: We will define the spectrum of a quantum graph and then study what information about the graph is contained
in the spectrum and vice versa. We will show that isospectral quantum graphs exist but that isospectral sets are finite. We
will introduce the more general notion of the Floquet spectrum and ask whether the same effects still occur.
Room Number: S2 145
Name: Kronholm, Brandt
University: University of Albany
Email: jk174783@albany.edu
Title: Ramanujan Congruence Properties of the Restricted Partition Function p(n, m).
Abstract: The restricted partition function p(n,m) enumerates the number of partitions of n into exactly m parts. The
relationship between the unrestricted partition function p(n) and p(n, m) is clear:
p(n) = p(n, 1) + p(n, 2) + ... + p(n, n).
Ramanujan’s partition congruences are well known: p(5n + 4) ≡ 0 (mod 5), p(7n + 5) ≡ 0 (mod 7), etc.. Ono (2000) proved
that there are Ramanujan congruences for p(n) for every prime ' > 3. In 2005, the speaker showed that there are Ramanujan
congruences for p(n, m) for every prime m = ' ≥ 3. In this talk we will discuss a Ramanujan-like congruence relation for
p(n,m) where for our choice of prime ' there is no restriction on n. We shall also discuss a Ramanujan-like congruence
relation for p(n,m) where there are no restrictions on either n nor m.
Room Number: SL 206
4
Name: Feingold, Alex
University: Binghamton University
Email: alex@math.binghamton.edu
Title: Historial Perspectives on Vertex Operator Algebras
Abstract I will present some of the history of the development of the theory of vertex operator algebras, how the first
vertex operators were used to represent affine Kac-Moody Lie algebras in the principal and homogeneous pictures, and then
extended to include operators representing the Virasoro algebra. Special constructions (bosonic from a lattice and fermionic
from Clifford algebras) show common features which can be abstracted as the axioms of a vertex operator algebra.
Room Number: SL 210
Presentations at 3:20pm on Saturday
Name: Evren, Ozgur
University: CUNY Graduate Center
Email: oevren@gc.cuny.edu
Title: Two Metrics on Teichmuller Space
Abstract: Given a hyperbolic Riemann surface, there are two distinct distance functions on the Teichmuller space of the
surface; namely the length spectrum distance and the Teichmuller distance. For the surfaces of finite type, it is known that
these two distances determine the same topology. In his paper, ”On a Distance Defined by the Length Spectrum on Teichmuller Space”, H. Shiga shows that there exists a Riemann surface of infinite type such that the length spectrum distance
does not define the same topology as the Teichmuller distance on the Teichmuller space of the surface. In this talk, after a
brief introduction to quasi-conformal mappings and Teichmuller spaces, we will focus mostly on this result. Time permitting,
we will discuss additional results from the same paper, such as the incompleteness of the length spectrum distance and a
sufficient condition for the length distance to define the same topology as that of the Teichmuller distance.
Room Number: S2 140
Name: Schneider, Greg
University: University at Buffalo, SUNY
Email: grs4@buffalo.edu
Title: Box-Dot Diagrams for ”Regular” Rational Tangles
Abstract: We introduce a new presentation for rational tangles which illustrates a geometric connection to the number theory of positive regular continued fractions. This presentation also admits a suitable extension to the contact setting, allowing
us to define a natural Legendrian embedding of a particular class of rational tangles into the standard contact Euclidean
3-space. We will briefly discuss how these box-dot diagrams, along with an associated construction, can be used to determine
when the Legendrian flyping operation yields tangles which are not Legendrian isotopic, further refining an earlier result of
Traynor.
Room Number: S2 145
Name: Petrenko, Bogdan
University: SUNY Brockport
Email: bpetrenk@brockport.edu
Title: Probability of generating an algebra
Abstract: I will explain a method of calculating the probability that several random elements generate a given algebra
(whose additive group is assumed to be free Abelian of finite rank). I will illustrate this method by computing the probability
that several random elements generate the Lie algebra sl2 (Z). My talk will be based on joint work with Rostyslav Kravchenko
and Marcin Mazur.
Room Number: SL 206
Name: Robinson, Thomas
University: Rutgers
Email: thomasro@math.rutgers.edu
Title: One dimensional vertex algebras
Abstract: We shall present a few proofs of the existence of one dimensional vertex algebras.
Room Number: SL210
5
Presentations at 4:10pm on Saturday
Name: Atchison, Ben
University: University of Albany
Email: ba577642@albany.edu
Title: Shift Automorphisms of a Free Group
Abstract: A shift automorphism α of the free group Fn is an automorphism with the property that α(xi ) = xi+1 for
1 ≤ i ≤ n − 1, and some basis {x1 , ..., xn } of Fn . We considered the problem of classifying shift automorphisms of finite outer
order. The motivation for this is the analogy with rational canonical forms for matrices.
Room: S2 145
Name: Xiao, Xiao
University: Binghamton University
Email: xiao@math.binghamton.edu
Title: Introduction to F-crystals
Abstract: Let k be an algebraically closed field of characteristic p, W(k) the ring of Witt vectors. An F-crystal over k is a
pair (M,phi) where M is a free W(k)-module and phi is an injective Frobenius linear endomorphism of M. In this talk, I will
discuss some basic properties of F-crystals from examples and describe its background in arithmetic algebraic geometry. If
time permits, I will briefly introduce some old and new results of its classification in some interesting cases.
Room Number: SL 206
Name: Axtell, Jonathan
University: University of Connecticut- Waterbury
Email: axtell@math.uconn.edu
Title: Vertex Operator Algebras for Type G Affine Lie Algebras
Abstract: We discuss some results on the classification of certain Vertex Operator Algebras (VOA) associated with affine
Lie algebras of type G2 . The VOA we consider arise from a certain generalization of integrable modules, first considered by
V. Kac and M. Wakimoto. The resulting VOA can be viewed as a generalization of rational VOA.
Room Number: SL 210
Presentations at 4:50pm on Saturday
Name: Rathbun, Matt
University: University of California, Davis
Email: mrathbun@math.ucdavis.edu
Title: High Distance Knots in Any 3-Manifold
Abstract: This is joint work with Marion Moore. Let M be a closed 3-manifold with a given Heegaard splitting. We show
that after a single stabilization, some core of the stabilized splitting has arbitrarily high distance with respect to the splitting
surface. This generalizes a result of Minsky, Moriah, and Schleimer for knots in S 3 . We also show that in the complex of
curves, handlebody sets are either coarsely distinct or identical. We define the coarse mapping class group of a Heeegaard
splitting, and show that if (S, V, W ) is a Heegaard splitting of genus ≥ 4, then CMCG(S,V,W) ∼
= MCG(S,V,W).
Room Number: S2 140
Name: Vogeler, Roger
University: CCSU
Email: rvogeler@gmail.com
Title: Exceptional non-CAT(0) polygonal complexes
Abstract: I will describe some exotic polygonal complexes, including the evil twin of the hypercube, and explain the grouptheoretic technique by which they are constructed.
Room Number: S2 145
6
Name: Zaremsky, Matthew
University: University of Virginia
Email: mcz5r@virginia.edu
Title: VRGD systems and affine buildings
Abstract: Given a field K with discrete valuation, the group SL2 (K) admits a canonical action on an associated tree. This
situation can be vastly generalized with the theory of VRGD systems: a group that admits a VRGD system has a natural
action on an associated affine building. In this talk I will axiomatize VRGD systems and affine buildings and explain how
this natural action arises. If time permits I will mention some recent results regarding transitivity properties of these group
actions.
Room Number: SL 206
Name: Wiesner, Emilie
University: Ithaca College
Email: ewiesner@ithaca.edu
Title: Whittaker Modules for the Virasoro Algebra
Abstract: Whitaker modules were first defined for classical Lie algebras. Although they are not weight modules, they still
take advantage of the triangular decomposition of these algebras. This leads to natural generalizations to other Lie algebras
with triangular decomposition. I will talk about Whittaker modules in the context of the Virasoro algebra.
Room Number: SL 210
Presentations at 9:20am on Sunday
Name: Hoang, Quang
University: University of Vlora
Email: hoang@univlora.edu.al
Title: Cohomology of some torsion free nilpotent groups
Abstract: Let Un be the group of (n + 1) × (n + 1) upper triangular matrices with integer entries and 1’s on diagonal.
We study the cohomology ring of some torsion free nilpotent groups Vn , where Vn is the quotient of Un by the subgroup
consisting of matrices with 0’s on the two “diagonals” above the diagonal. A system of generators is given. However, the full
set of relations is not known and is proposed as an open question.
Room Number: S2 140
Name: Short, Matt
University: Binghamton University
Email: short@math.binghamton.edu
Title: Nonisomorphism or: How I learned to stop worrying and love Germs
Abstract: The question is easy to ask: Given two subgroups of the group(s) of homeomorphisms of a (or two) topological
spaces, are they isomorphic? In general the question is difficult to answer. In this talk I will explain a result of Mati Rubin
which helps us to determine when they not, and show how this result was used by Brin, and then Bleak/Lanoue to show
nonisomorphism of the higher dimensional Thompson groups with the other families of Thompson groups.
Room Number: S2 145
Name: Lee, Kristopher
University: Clarkson University
Email: leekm@clarkson.edu
Title: Characterizing Isomorphisms Between Algebras
Abstract: There is a long history of analyzing maps between algebras. In 1897, Fröbenius studied linear maps T : Cn×n →
Cn×n that preserve determinant and showed that such maps were multiplicative or anti-multiplicative. This was the first
example of what has become to be known as a linear preserver problem. Another result of this type was given by Marcus
and Purves, who showed that a linear map T : Cn×n → Cn×n that preserves invertible matrices and preserves the identity
must satisfy T (A2 ) = T (A)2 . A natural extension to linear preserver problems is to drop the assumption of linearity. We
will discuss problems of this type and present recent work that has been done in function algebras. In particular, we will see
how the underlying topology has a large impact on methods of this work.
Room Number: SL 206
7
Name: Greenough, Justin
University: University of New Hampshire
Email: jrg8@cisunix.unh.edu
Title: Monoidal 2-categories, Rep(G)-modules and de-equivariantization
Abstract: Using tensor product we can “multiply” modules to obtain new modules. It is possible to do something similar on
a categorical level, to “multiply” module categories to obtain new ones. In recent work we have shown that with this product
the 2-category of C-bimodule categories for fixed tensor category C is a monoidal 2-category in the sense of Kapranov and
Voevodsky. We provide a monoidal-structure preserving 2-equivalence between the 2-category of C-bimodule categories and
module categories over the center of C. As an application we explicitly determine Rep(G)-module fusion rules for finite group
G and use this to show that the group of irreducible Rep(G)-module categories is isomorphic to H 2 (G, k × ), generalizing
results of Etingof, Nikshych and Ostrik. We also explain de-equivariantization of tensor categories containing Rep(G) and
show that it corresponds canonically to categorical tensor product in a way that preserves tensor structure.
Room Number: SL 210
Presentations at 11:20am on Sunday
Name: Sultan, Harold
University: Columbia University
Email: haroldsultan@gmail.com
Title: Geometric Thickness of the Pants Complex
Abstract: Excluding the genus two surface with one puncture, the thickness of all surfaces of finite type are known, and in
fact are determined by their topological complexity, by the combined work or Behrstock-Drutu-Mosher, and Brock-Masur.
For the case of S2,1 , the combine work of the above authors is enough to show that the pants graph of the surface is thick of
order at least 1 and at most 2. In my talk I will outline the approaches of the previous authors and present my research in
progress toward the fact that P(S2,1 ) is thick of order precisely 1.
Room Number: S2 140
Name: Thompson, Russ
University: Cornell
Email: thru@math.cornell.edu
Title: Amenability and the Poisson boundary
Abstract: There are several notions of the boundary of a finitely generated group. The aim of this talk is to introduce the
Poisson boundary, P(G, µ), of a finitely generated group with probability measure µ. The Poisson boundary can be defined
in terms of the asymptotic behavior of random walks on G, and is thus related to amenability. Of particular interest is that
the Poisson boundary is a finer concept than amenability. We will discuss this relationship and some interesting examples.
Room Number: S2 145
Name: Vasiu, Adrian
University: Binghamton University
Email: adrian@math.binghamton.edu
Title: Boundedness results for finite flat group schemes over discrete valuation rings of mixed characteristic
Abstract: Let p be a prime. Let V be a discrete valuation ring of mixed characteristic (0, p) and index of ramification e.
A classical theorem of Raynaud says that if e < p − 1, then each commutative finite flat group scheme of p power order over
V is uniquely determined by its generic fibre over the field of fractions of V. In this talk we report on the generalization of
this result to arbitrary indexes of ramification e. This generalization allows to reobtain and strengthen a classical extension
theorem of Tate for p-divisible groups. This is joint work with Thomas Zink (Bielefeld University).
Room Number: SL 206
8
Name: Cahn, Patricia
University: Dartmouth College
Email: patricia.cahn@dartmouth.edu
Title: A Generalization of the Turaev Cobracket and the Minimal Self-Intersection Number of a Curve on a Surface
Abstract: Goldman and Turaev constructed a Lie bialgebra structure on the vector space generated by free homotopy
classes of loops on a surface. The Turaev cobracket gives a lower bound on the minimal number of self-intersection points of
a loop in a given homotopy class. Chas proved that this lower bound is not sharp by providing examples of homotopy classes
with zero cobracket that do not contain a simple representative. The Turaev cobracket factors through another operation µ,
defined in the spirit of the Andersen-Mattes-Reshetikhin algebra. The operation µ also gives a lower bound on the minimal
number of self-intersection points of a loop in a given homotopy class. We will show that this lower bound is sharp for
homotopy classes α that do not contain a power of a curve. In particular, we show that the sum of the absolute values of
the coefficients of µ(α) is always twice the minimal number of self-intersection points of a loop in α.
Room Number: SL 210
Presentations at 12:00pm on Sunday
Name: Burke, John
University: Wesleyan Univeristy
Email: jrburke@wesleyan.edu
Title: The Concordance Group of Knots
Abstract: A knot in S 3 is considered smoothly slice if it bounds a smooth disk in B 4 . This notion leads to defining the
equivalence relation of concordance on the set of knots. I will define a binary operation on the equivalence classes of this
relation which will then define the concordance group. During the talk, I will discuss motivations for studying concordance,
and time permitting, current work concerning concordance.
Room Number: S2 140
Name: Staley, Daniel
University: Rutgers University
Email: staley@math.rutgers.edu
Title: Weird Quasi-Geodesic Behavior at Infinity
Abstract: CAT(0) spaces are spaces that satisfy a certain notion of nonpositive curvature. A group with a geometric
action on a CAT(0) space is called a CAT(0) group, and there’s lots of interesting theorems about such groups. One of the
interesting features of a CAT(0) space is that it has a visual boundary consisting of geodesic rays emitting from a particular
basepoint. Unfortunately, unlike a hyperbolic boundary, a CAT(0) boundary is not an invariant of the group acting on the
space, i.e., the same group can act on spaces with different boundaries. I’ll present a result which shows how these boundaries
”go wrong” when you try to map one to the other.
Room Number: S2 145
Name: Johnson, John
University: Howard University
Email: john.j.jr@gmail.com
Title: Connections between the two notions of Partition Regular Matrices
Abstract: There are two notions of partition regularity. An m × n matrix A with entries from Z is called kernel partition regular if and only if whenever N is finitely colored, there exist monochromatic x1 , . . . , xn such that Ax = 0 where
x = (x1 , . . . , xn ). Similarly, a m × n matrix B with entries form Z is image partition regular if and only if whenever N is
finitely colored, there exists y ∈ Nn such that all the entries in By are monochromatic. I will be talking about the connections
between these two notions of partition regularity.
Room Number: SL 206
9
Name: Goldstein, Ellen
University: Tufts University
Email: ellen.goldstein@tufts.edu
Title: Normality of Closures of Conjugacy Classes in Classical Groups
Abstract: Given an algebraic group G and its Lie algebra, g, the Zariski closure of the adjoint orbit Gx for x ∈ g is a
subvariety of g. If G = GL(V ) for V a finite dimensional vector space over an algebraically closed field K, Gx is a normal
variety for x ∈ g = Mn (K) for K of arbitrary characteristic. If G = O(V ) or Sp(V ), Kraft and Procesi proved that Gx is
normal for some x ∈ o(V ) or sp(V ) in the case where K has characteristic 0. One would like to know for which x Gx is
normal in arbitrary characteristic ("= 2). One component of this problem is generalizing a codimension formula for a nilpotent
orbit in Gx \ Gx, which will be used to show that, for the majority of x, Gx is a normal variety.
Room Number: SL 210
This conference is supported by National Science Foundation Grant No. DMS0946269 and several Binghamton University departments and organizations including the Mathematics Department, Office of the Vice President for Research,
Convocations Committee, Harpur Dean’s Office, and the Graduate School. Any opinions, findings and conclusions or recommendations expressed here are those of the author(s) and do not necessarily reflect the views of the National Science
Foundation (NSF) or any other sponsor.
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