| Sept 10 |
Bart Van Steirteghem, FAU Erlangen-Nürnberg and CUNY,
Momentum
polytopes of projective spherical varieties |
| |
|
| Sept 17 |
Khalid Bou-Rabee, City College and the CUNY Graduate Center,
Quantifying residual finiteness |
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|
| Sept 24 |
No Seminar |
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|
| Oct 1 |
Holiday – No Seminar |
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|
| Oct 8 |
Holiday – No Seminar |
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|
| Oct 15 |
Corina Calinescu, NY City Tech and the CUNY Graduate Center,
On
Applications of Vertex Algebras to Partitions of Numbers |
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|
| Oct 22 |
Amita Malik, Rutgers, Zeros of derivatives of the completed
Riemann zeta function |
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|
| Oct 29 |
Bianca Santoro, City College and the CUNY Graduate Center,
Bifurcation of periodic solutions to the singular Yamabe problem on
spheres |
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|
| Nov 5 |
Philipp Rothmaler, BCC and the CUNY Graduate Center,
High and
low formulas in modules |
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|
| Nov 12 |
Uma Iyer, BCC and the CUNY Graduate Center, The algebra of
Integro-Differential operators |
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|
| Nov 19 |
Karen Taylor, BCC, Quadratic identities and Theta Series
attached to Quadratic Fields |
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|
| Nov 26 |
Philip Ording, Sarah Lawrence College, What we talk about
when we talk about writing |
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|
| Dec 3 |
Luis Fernandez, BCC and the CUNY Graduate Center,
Why does the occidental musical scale have 12 notes? |
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|
| Dec 10 |
Aleksandar Milivojevic, Stony Brook University,
The rational topology of closed almost complex
manifolds |
| Feb 12 |
Holiday – No Seminar |
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|
| Feb 19 |
Roman Kossak, BCC and the CUNY Graduate Center,
Kernels of
directed graphs (and some logic) |
| |
|
| Feb 26 |
Ronnie Nagloo, BCC, The Ax-Lindemann-Weierstrass theorem and the
Fuchsian automorphic functions |
| |
|
| Mar 5 |
Karen Taylor, BCC, Dirichlet Series and Generalized Hecke Groups |
| |
|
| Mar 12 |
Corey Switzer, the CUNY Graduate Center, Independence in
Arithmetic and Non-Standard Combinatorics |
| |
|
| Mar 19 |
Scott Wilson, Queens College and the CUNY Graduate Center,
Some
problems and recent progress related to almost complex manifolds |
| |
|
| Mar 26 |
Alex Martsinkovsky, Northeastern University, From Torsion to
Cotorsion and Back |
| |
|
| Apr 2 |
Gleb Pogudin, Courant NYU, Primitive Element Theorem for fields
with commuting derivations and automorphisms |
| |
|
| Apr 9 |
Ethan Cotterill, Federal Fluminense University, Brazil,
Real
inflection points on real (hyper)elliptic curves |
| |
|
| Apr 16 |
Zhe Wang, BCC, An example of Lebesgue invariant Markov
partitions and its Beurling-Ahlfors quasiconformal extension |
| |
|
| Apr 23 |
Spring Break – No Seminar |
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|
| Apr 30 |
Kevin O’Bryant, College of Staten Island and the CUNY Graduate
Center, Rational Approximation: Numbers, Functions, and Numbers
Again |
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|
| May 7 |
Mingxian Zhong, Lehman College, Two recent results on coloring
graphs with forbidden induced subgraphs |
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|
| May 14 |
The Stanley Friedlander Lecture, Dennis Sullivan,
CUNY Graduate Center and Stony Brook University,
A notion of
geometry that includes many more three dimensional manifolds |
Title:
Momentum polytopes of projective spherical varieties
Speaker: Bart Van Steirteghem, FAU Erlangen-Nürnberg and CUNY
Tuesday, Sept 10
Abstract: Spherical varieties
are a natural generalization of toric varieties, where the acting torus
is replaced by a general connected reductive group. They also include
flag varieties and symmetric varieties. Using examples, I will explain
how their rich combinatorics allows us to characterize the momentum
polytopes of projective spherical varieties. I will also discuss an
application to the Kählerizability problem for compact multiplicity free
Hamiltonian manifolds. This is joint work with S. Cupit-Foutou and G.
Pezzini. |
| |
Title: Quantifying residual finiteness
Speaker:
Khalid Bou-Rabee, City College CUNY
Tuesday, Sept 17
Abstract: The theory
of quantifying residual finiteness assigns, to each finitely generated
group, an invariant that indicates how well-approximated the group is by
its finite quotients. We introduce this theory and survey the current
state of the subject. There will be a strong emphasis on examples, open
questions, and connections to other subjects. |
| |
Title:
On Applications of Vertex Algebras to Partitions of Numbers
Speaker: Corina Calinescu, NY City Tech and the CUNY Graduate
Center
Tuesday, Oct 15
Abstract: A
remarkable feature of the theory of vertex algebras has been its
connection to Lie algebras, combinatorics and modular forms, which lead
to fundamental results and conjectures in mathematics. Standard modules
and certain subspaces, called principal subspaces, for affine
Lie algebras have vertex operator constructions. These constructions
have been studied in conjunction with combinatorial identities, such as
the Rogers-Ramanujan partition identities. This talk is based on joint
works with Lepowsky, Milas, Penn and Sadowski. |
| |
Title: Zeros of derivatives of the completed Riemann zeta function
Speaker: Amita Malik, Rutgers
Tuesday, Oct 22
Abstract: In his only paper from 1859 in Number
Theory, Riemann studied the function that is now known as
the completed Riemann zeta function. He stated that the zeros of
this function are expected to lie on the critical line. Under this
assumption, it can be shown that the zeros of its derivatives also lie
on the critical line. In this talk, we discuss the vertical distribution
of these zeros and prove discrepancy results analogous to those of the
original function. If time permits, we show that in the limiting case,
100% of the zeros of certain combinations of these derivatives lie on
the critical line in the spirit of Conrey's results on the zeros of
these derivatives. |
| |
Title: Bifurcation
of periodic solutions to the singular Yamabe problem on spheres
Speaker: Bianca Santoro, City College and the Graduate Center
Tuesday, Oct 29
Abstract: In this talk, we describe how to obtain
uncountably many periodic solutions to the singular Yamabe problem on a
round sphere that blow up along a great circle. These are complete
constant scalar curvature metrics on the complement of S^1 inside S^m, m
≥ 5, conformal to the round metric and periodic in the sense of being
invariant under a discrete group of conformal transformations. These
solutions come from bifurcating branches of constant scalar curvature
metrics on compact quotients of S^m \ S^1. This is a joint work with R.
Bettiol (Lehman College) and P. Piccione (USP-Brazil). |
| |
Title: The algebra
of Integro-Differential operators
Speaker: Uma Iyer, BCC and
the CUNY Graduate Center
Tuesday, Nov 12
Abstract: This
algebra has been introduced and studied by V. Bavula. This algebra
contains the Weyl algebra. I will talk about this algebra and a little
bit about its representation theory (studied by Futorny, Bekket,
Bavula). I will then introduce some questions for further study. |
| |
Title: Quadratic
identities and Theta Series attached to Quadratic Fields
Speaker: Karen Taylor, BCC
Tuesday, Nov 19
Abstract: We will
discuss identities between solutions to the generalized Pell's equation
obtained from the coincidence of Theta series. Our emphasis will be on
examples found in the literature. |
| |
Title: What we talk
about when we talk about writing
Speaker: Philip Ording,
Sarah Lawrence College
Tuesday, Nov 26
Abstract: What
qualities does mathematical writing exhibit? Is it possible to describe
the ways that mathematicians write independent of what they prove? And
if so, how? Why do some writerly terms appear more relevant (e.g. style)
than others (e.g. voice)? What might these loan words bring to a
mathematical context from writing and criticism elsewhere? The goal of
this talk is to motivate these questions through vivid examples, most of
which I encountered while writing the book '99 Variations on a Proof' in
the wilds of the math landscape, past and present. |
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Title: Why does the
occidental musical scale have 12 notes?
Speaker: Luis
Fernandez, BCC and the CUNY Graduate Center
Tuesday, Dec 3
Abstract: If we look at a piano keyboard we see that there is a pattern
of 12 consecutive (white and black) notes. Why 12? What is the relation
between consecutive notes? How was this scale constructed?
There is a
purely mathematical explanation of this fact. I will explain why the
12-note chromatic scale, as well as the pentatonic scale, appear
naturally. I will also show the construction of our current equal
temperament chromatic scale.
Disclaimer: This will not be a research
talk. It will be an expository talk and the only prerequisites are
logarithms and a very basic knowledge of modular arithmetic, so it is
appropriate for math majors. And I am pretty sure it will be fun. |
| |
Title: The rational
topology of closed almost complex manifolds
Speaker:
Aleksandar Milivojevic, Stony Brook University
Tuesday, Dec 10
Abstract: Given an even-dimensional oriented closed smooth manifold,
there are topological obstructions to it admitting an almost complex
structure (i.e. an endomorphism of its tangent bundle that squares to
-1). The most prominent of these come from (a) the requirement that the
total Pontryagin class must have a “square root” in the form of the
Chern class, and (b) various congruences among the tentative Chern
numbers coming from Hirzebruch-Riemann-Roch/Atiyah-Singer.
If we
start with only a (simply connected) topological space with no
additional structure, we can ask whether there exists a closed almost
complex manifold rationally equivalent to the space (i.e. admitting a
map to a “rationalized” version of the space which induces an
isomorphism on rational homology). A first necessary condition is that
the space satisfies Poincare duality on its rational cohomology, giving
it a rational cohomological dimension which we will assume is at least
six. If this topological space can support “Chern classes” in its
rational cohomology whose associated Chern numbers satisfy the
congruences from point (b) above, along with some further conditions on
the middle degree nondegenerate pairing if the dimension is divisible by
4, then there is indeed such a closed almost complex manifold with these
Chern classes. I will elaborate on this result and illustrate how
number-theoretic problems quickly enter the discussion. |
| |
Title: Kernels of
directed graphs (and some logic)
Speaker: Roman Kossak
Tuesday, Feb 19
Abstract: I will outline the proof of the
following recent theorem due to James Schmerl: Every resplendent
directed acyclic graph having local finite height has a kernel.
If
time permits, I will discuss an application of the theorem to a problem
in model theory of arithmetic. For a definition and a short discussion
of resplendent structures see
https://www.ams.org/notices/201106/rtx110600812p.pdf |
| |
Title: The
Ax-Lindemann-Weierstrass theorem and the Fuchsian automorphic functions
Speaker: Ronnie Nagloo
Tuesday, Feb 26
Abstract: In this talk,
I will discuss recent work, joint with G. Casale and J. Freitag, around
the problem of transcendence of the Fuchsian automorphic functions.
These are the uniformizing functions for compact Riemann surfaces of
genus zero that are obtained from quotients of the upper half plane by
certain Fuchsian groups (a well-known example is the modular
j-function).
I will place particular emphasis on the so called
Ax-Lindemann-Weierstrass theorem and on a conjecture of Painlevé (1903)
which this work resolves. If time permits, I will also explain how our
work can be applied to answer a question in number theory (or more
precisely to tackle an instance of the special points conjectures). |
| |
Title: Dirichlet
Series and Generalized Hecke Groups
Speaker: Karen Taylor
Tuesday, March 5
Abstract: Duke introduce the groups G(A) which
naturally correspond to an ideal class, A, of a real quadratic field.
These groups generalize the Hecke groups G(lambda), lambda>2. In this
talk, I will describe two problems, which have been solved for the Hecke
groups, and which I am currently working on generalizing. One problem,
solved by Rosen, is the description of the elements of G(lambda) by
continued fractions. The other is to prove the appropriate form of the
Riemann-Bochner-Hecke converse theorem. |
| |
Title: Independence
in Arithmetic and Non-Standard Combinatorics
Speaker: Corey
Switzer, the CUNY Graduate Center
Tuesday, March 12
Abstract:
Peano Arithmetic (PA) is the formalization of finite mathematics in
first order logic. The standard model of PA is simply the natural
numbers with their normal operations. However, in the setting of model
theory, there are also non standard models of PA: discretely ordered
semi-rings with infinite descending chains satisfying a version of
induction. The existence of such models opens up the possibility of
statements independent of arithmetic: true statements about the natural
numbers not provable from standard finite methods. In this talk we will
show how such statements are found and give some examples. Time
permitting we'll discuss our recent work on (L, n)-models which codify
such independence results. |
| |
Title: Some
problems and recent progress related to almost complex manifolds.
Speaker: Scott Wilson, Queens College and the CUNY Graduate Center
Tuesday, March 19
Abstract: An almost complex manifold is a
smooth manifold whose tangent bundle has the structure of a complex
vector bundle. Many interesting examples appear in complex geometry and
symplectic topology. A fair amount is known concerning when a manifold
has one of these structures, and yet there remain many important and
illusive open questions. In this talk I'll survey some elementary
results while exploring these questions, and report on some recent
progress which develops new algebraic and analytic methods for studying
these objects. |
| |
Title: From Torsion
to Cotorsion and Back
Speaker: Alex Martsinkovsky,
Northeastern University
Tuesday, March 26
Abstract: The notion
of torsion is known to everybody who has ever seen an abelian group. The
notion of cotorsion is not known to anybody; in fact, it doesn’t even
exist. This claim does not contradict the fact that there are 597
entries in MathSciNet containing the word cotorsion. The goal of this
talk is to explain this paradox and give the correct definition of
cotorsion. To do this, we have to rethink the classical definition of
torsion and generalize it to arbitrary rings and modules. The definition
of cotorsion will also be done in complete generality — for arbitrary
modules over arbitrary rings. The two concepts turn out to be related by
a duality.
This is an expository talk and prerequisites are modest:
basic properties of the tensor product and the Hom functors. I will
freely use the notions of projective and injective modules and of
derived functors, but these will be reviewed at the beginning of the
lecture.
This is joint work with Jeremy Russell. |
| |
Title: Primitive
Element Theorem for fields with commuting derivations and automorphisms
Speaker: Gleb Pogudin, Courant NYU
Tuesday, April 2
Abstract:
Primitive Element Theorem says that every finitely generated algebraic
extension of fields of zero characteristic is generated by a single
element. It is a fundamental tool in algebra and symbolic computation.
When we talk about fields generated by solutions of differential or
difference equations, the field extensions obtained by adjoining the
solutions of these equations are not longer algebraic. On the other
hand, these field extensions have extra structure, namely differential
or difference operators, and this structure might give us additional
expressive power. Appropriate generalizations of the Primitive Element
Theorem to field extensions equipped with commuting derivations or a
difference operator were obtained by Kolchin (1942) and Cohn (1965),
respectively.
In my talk, I will describe my recent result that
generalizes theorems by Kolchin and Cohn in two directions
simultaneously
1. Any number of derivations and difference operators
is allowed given that they commute with each other;
2. All
restrictions on the base field are removed. This makes the theorem
applicable to many new important cases, for example, to extensions
coming from autonomous equations. |
| |
Title: Real
inflection points on real (hyper)elliptic curves
Speaker:
Ethan Cotterill, Federal Fluminense University, Brazil
Tuesday, April
9
Abstract: Understanding when a given abstract algebraic curve
comes equipped with a degree-d embedding in r-dimensional projective
space is a fundamental problem of algebraic geometry. A crucial
subsidiary issue is how inflected the curve C is under a given
projective embedding. When our curve is defined over the complex
numbers, a celebrated classical result of Plucker establishes that the
degree of total inflection is an explicit function of d, r, and the
genus g of C. In this talk we will examine what Plucker-like analogues
hold when we work over the real instead of complex numbers, and assuming
that C is of hyperelliptic type. If time permits, we will also comment
on generalizations to other base fields. (Joint with I. Biswas and C.
Garay López) |
| |
Title: An example
of Lebesgue invariant Markov partitions and its Beurling-Ahlfors
quasiconformal extension
Speaker: Zhe Wang, BCC
Tuesday,
April 16
Abstract: I will use an example to explain a research
project with Yunchun Hu and Yunping Jiang (Queens College). We are
working on symmetric conjugacy classes of uniformly quasisymmetric
expanding covering maps of the unit circle. We want to show the
uniqueness of the Lebesgue invariant map in each conjugacy class. |
| |
Title: Rational
Approximation: Numbers, Functions, and Numbers Again
Speaker: Kevin O'Bryant, College of Staten Island and the CUNY Graduate
Center
Tuesday, April 30
Abstract: Quantifying the density of
rationals in the reals is a fundamental problem. Given a real number
$x$, there are rationals close to it with large denominator, but what
exactly is the relationship between ``close to $x$’’ and ``large
denominator’’? Unsatisfying partial answers are given by measure theory,
continued fractions, and often beautiful complex function arguments. In
the last decades, the little-known theory of Pad\’e approximants
(approximating an analytic function with a rational function, as opposed
to with a mere polynomial) has provided concrete progress for a few $x$. |
| |
Title: Two recent
results on coloring graphs with forbidden induced subgraphs
Speaker: Mingxian Zhong, Lehman College
Tuesday, May 7
Abstract: Graph coloring is a fundamental problem in graph theory and
has a variety of applications. It is well known that deciding whether a
graph can be colored within k colors is NP-complete if k is at least 3.
Thus it is natural to ask whether the complexity of the problem changes
if we know that the input graph does not contain a particular induced
subgraph. In the first part of the talk, I will present a polynomial
time algorithm for the 4-coloring problem and the 4-precoloring
extension problem restricted to the class of graphs with no induced
six-vertex path, thus proving a conjecture of Huang. Combined with
previously known results this completes the classification of the
complexity of the 4-coloring problem for graphs with a connected
forbidden induced subgraph. This is joint work with Maria Chundnovsky
and Sophie Spirkl. In the second part of the talk, I will discuss the
the case when the forbidden graph is not connected. Specficically, I
will present a polynomial tiame algorithm of list-three coloring on
$P_6+rP_1$-free grpahs. This is joint work with Maria Chundnovsky,
Shenwei Huang and Sophie Spirkl. |
| |
Title: A notion of
geometry that includes many more three dimensional manifolds
Speaker: Dennis Sullivan, CUNY Graduate Center and Stony Brook
University
Tuesday, May 14
Abstract: Beyond Riemann's notion
of geometry, one has projective geometry on projective space which in
turn can be generalized to coset spaces of any Lie group, Ehresmann
1950. The lecture will describe an extension of the verified
Thurston-Poincaré conjecture that is possible because of further
structure in that information (joint work with Alice Kwon, PhD CUNY
2019). The last main point of this work is to extend the scope of the
Ehresmann conception of geometry to profit from the extra information
mentioned above. Then all prime three manifolds will have geometry. |