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## Seminars, Colloquia, and Conferences
Seminars |
## Seminars, Colloquia, and Conferences## ColloquiaThe colloquium meets on ## Fall 2018September 7Zhengwei Liu, Harvard University Title: Quantum Fourier AnalysisAbstract: We first recall some classical
inequalities and uncertainty principles in Fourier analysis. Then we
discuss our recent work on Fourier analysis in various subjects,
including subfactors, planar algebras, Kac algebras, locally compact
quantum groups, modular tensor categories. Moreover, we provide a 2D
picture language to study Fourier analysis. Finally, we discuss some
applications and open questions.September 14No colloquium this week.September 21Christina Sormani, CUNY Title: Abstract: The spacelike universe is curved by gravity
forming deep wells around massive objects. A black hole is formed
when it is curved so strongly that a neck forms and the apparent
horizon is the minimal sphere around that neck. The ADM mass of an
asymptotically flat region in space is measured by the decay of the
curvature near infinity. Shing-Tung Yau and Richard Schoen proved
that in such spaces the ADM mass must be nonnegative, and if the ADM
mass is 0 then the space is flat Euclidean space with no curvature
at all. Here we present recent joint work with Dan Lee, Lan-Hsuan
Huang, and Iva Stavrov proving that in special settings, spaces with
small ADM mass are almost Euclidean space. All students who have
completed vector calculus are welcome to attend.September 28Anna Haensch, Duquesne University Title: 17 Facts About Science Writing That Will Totally
Blow Your MindAbstract: Scientists are always doing research.
Occasionally, they do something catchy and it gets covered by the
mainstream media. I'm going to talk about how that science gets from
the lab bench to the Twitter feed, and trace the evolution of facts
as science becomes journalism and what gets lost and gained along
the way. Next, I'll show you all the ways that math and science
actually show up in mainstream journalism even when the stories have
nothing to do with science! Finally, I'll make the case for
scientific and numerical literacy as a necessary skill for
understanding the news, promoting social justice and participating
in the democratic process.October 5 *NOTE: Talk will be held in Science & Engineering
Complex (SEC), Anderson Room 206*Shing-tung Yau, Harvard University Title: Quasilocal Mass in General Relativity Abstract: I will talk about the problem of defining
conserved quantities in general relativity and explain their
properties.October 12Student Presentations from the Directed Reading Program Eva Sachar (graduate student mentor: Casey Cavanaugh) Title: An Application of Clustering to Socioeconomic DataAbstract: When analyzing socioeconomic data we wish to
uncover its inherent and underlying structure. We will be presenting
a few approaches to clustering and discussing their advantages and
disadvantages when applied to a housing dataset, and see if the
results of clustering on property characteristics and census block
demographics accurately reflect tiering in housing prices.Carter Silvey (graduate student mentor: Matthew Friedrichsen) Title: Fractal GeometryAbstract: Fractals are some of the most beautiful and
mysterious things to come out of mathematics. I’m going to discuss
the geometry behind these fractals, such as how they are created and
their dimensions. Specifically, I will talk about the Middle Third
Cantor Set, Julia Sets, and the Mandelbrot Set as well as some
applications that fractal geometry has in both the realm of
mathematics and the real world.October 19Michael Geline, Northern Illinois University Title: The conjectures of Brauer's block theory, and the
role of integral representationsAbstract: Frobenius's local to global principle for finite
groups asserts that properties of G, related to a prime p, should be
controlled by analogous properties of normalizers of proper
p-subgroups of G. Examples of properties of interest include the
existence of normal subgroups with index p and the existence of
irreducible representations with dimension divisible by a fixed
power of p. Brauer, Alperin, and Broue have given quite a few
specific conjectures of this nature which remain open to the present
day, partly because no one knows whether to expect proofs to depend
on the classification of finite simple groups. I will state several
of these conjectures and summarize how they have influenced my work
on p-adic representations.October 26 Dubi Kelmer, Boston College Title: Shrinking target problems, homogenous dynamics and
Diophantine approximationsAbstract: The shrinking target problem for a dynamical
system tries to answer the question of how fast can a sequence of
targets shrink so that a typical orbit will keep hitting them
indefinitely. I will describe some new and old results on this
problem for flows on homogenous spaces, with various applications to
problems in Diophantine approximations.November 2Daryl DeFord, MIT/Tufts University Title: Matched Products and Stirling Numbers of Graphs Abstract: In this talk I will introduce the matched product
for graphs, motivated by a popular construction for modeling
multiplex networks. The matched product depends on consistent
labelings of the nodes in the component graphs and recovers the
Cartesian, rooted, and hierarchical products as special cases. There
are natural conditions for the product to be planar, Hamiltonian,
and Eulerian in terms of the corresponding properties on the laers
and we will also consider the related problem of computing the
probability that a random relabeling of a given graph preserves each
property. In addition to these traditional graph-theoretic
properties, the matched product naturally defines several families
of graphs whose Stirling numbers of the first kind can be enumerated
in terms of the component values. We will see some explicit examples
of these families with combinatorial proofs in terms of the Pell
numbers and discuss a connection between this enumeration problem
and gerrymandering. November 9Jennifer Balakrishnan, Boston University Title: Rational points on the cursed curveAbstract: How do we compute rational points on curves? I'll
present a selection of techniques and motivating examples, from
antiquity to modern times. One particularly interesting example is
the split Cartan modular curve of level 13, also known as the
"cursed curve," a genus 3 curve defined over the rationals. By
Faltings' proof of Mordell's conjecture, we know that it has
finitely many rational points. However, Faltings' proof does not
give an algorithm for finding these points. We discuss how to
determine rational points on this curve using "quadratic Chabauty,"
part of Kim's nonabelian Chabauty program. This is joint work with
Netan Dogra, Steffen Mueller, Jan Tuitman, and Jan Vonk.November 16Bob Holt, University of Florida Title: Niche conservatism, evolution, and applied ecology:
Theoretical perspectivesAbstract: The Hutchinsonian niche of a species is defined
to be that set of abiotic and biotic conditions allowing it to
persist. Much of the diversity of life reflects evolution in
species' niches. The evolutionary record reveals a spectrum of rates
of change in species' and clade niches, from rapid niche evolution
to profound niche conservatism. Understanding the determinants of
evolution vs. conservatism in niches is of key importance in many
vital applied arenas, ranging from controlling the evolution of
resistance to pesticides and antibiotics, to facilitating
evolutionary rescue in species facing extinction in changed
environments. Theoretical studies of niche evolution with explicit
demography and genetics in spatially and temporally heterogeneous
environments can help illuminate when one might expect niche
conservatism, vs. evolution. This talk will provide an overview of
such studies. The mathematical topics touched upon will include how
demographic stochasticity can alter niche quantification, the use of
branching processes to illuminate niche evolution, and surprising
effects that emerge from the interplay of spatial processes and
temporal variability.November 30Carolyn Abbott, UC Berkeley Title: Random walks on groups acting on hyperbolic spacesAbstract: Imagine you are standing at the point 0 on a
number line, and you take a step forward or a step backwards, each
with probability 1/2. If you take a large number of steps, is it
likely that you will end up back where you started? What if you are
standing at a vertex of an 4-valent tree, and you take a step in
each of the 4 possible directions with probability 1/4? This process
is special case of what is called a random walk on a space. If the
space you choose is the Cayley graph of a group (as these examples
are), then a random walk allows you to choose a "random" or
"generic" element of the group by taking a large number of steps and
considering the label of the vertex where you end up. One can ask
what properties a generic element of the group is likely to have:
for example, is it likely that the element you land on has infinite
order? In this talk, I will discuss the algebraic and geometric
properties of generic elements of groups which act "nicely" on
hyperbolic metric spaces, with a focus on how such elements interact
with certain subgroups of the group. These results will apply to
generic elements of hyperbolic groups, relatively hyperbolic groups,
mapping class groups, many fundamental groups of 3—manifolds, the
outer automorphism group of a free group of rank at least two, and
CAT(0) groups with a rank one element, among many others. This is
joint work with Michael Hull.December 7Gianluca Caterina, Endicott College Title: The diagrammatic logic of C.S. Peirce: An approach
via generic figuresAbstract: At the turn of the 20th century, the American
philosopher and logician Charles Sanders Peirce developed a logical
system based on diagrams ("existential graphs") that capture the
essential features of what is currently know as first-order logic.
We will present an introduction to Peirce's work in logic, along
with a tentative model aimed to represent the existential graphs
within a category-theory framework. The talk will be accessible to undergraduates in both Mathematics and Philosophy. |
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