ColoState Math Department Colloquium 

Fall 2018 potential speakers:
(2) Catherine Good, Host: Jess Ellis
(1) Dev Sinha, University of Oregon, Host: Jeanne Duflot

Spring 2018:

Mon. 04/30, 4-5pm, Weber 223
Barbara Fantechi, Scuola Internazionale Superiore di Studi Avanzati (Italy)
Host: Renzo Cavalieri
Title:  Gromov Witten Invariants in Algebraic and Symplectic Geometry
Every nonsingular complex projective variety V is also a complex
manifold; in fact it is a symplectic manifold with a compatible complex
structure.  Gromov Witten invariants are defined both for smooth projective
varieties over an arbitrary algebraically closed field, and for compact
symplectic manifolds with a compatible almost complex structure.  We outline
differences and similarities in the definitions, and sketch ongoing attempts
to find a common language.

Mon. 04/16, 4-5pm, Weber 223
Leah Edelstein-Keshet, University of British Columbia
Host: Yongcheng Zhou
Title: Mathematical Models for Cell Shape: From One Cell to Many
The size and shape of a mammalian cell is regulated by a network
of proteins.  Among these are central regulators (GTPases) that control
the polarity, the contraction or the spreading of a cell.  In my talk, I
will describe efforts at understanding the emergent behaviour using
mathematical modeling at the level of a cell and of a tissue made up of
many cells.  The models lead to interesting mathematics, as well as
insights into behaviour observed in experimental cell biology.  I will
review both partial and ordinary differential equation versions of our
models, and illustrate some new methods devised to analyse these.  I will
conclude with recent work on waves of contraction observed in a tissue
composed of many "model cells".

Mon. 03/26, 4-5pm, Weber 223
Gideon Simpson, Drexel University
Host: David Aristoff
Title: Approaches to Metastability in Materials Science
One of the outstanding challenges in atomistic
simulations of materials is how to reach physically meaningful time
scales.  While the fundamental time scale of the atomistic models
is that of the femtosecond, physically meaningful phenomenon may
take microseconds or longer to occur.  This precludes a direct
numerical simulation with, for instance, a Langevin model of the
material from reaching physical time scales.  The time scale
separation challenge has motivated the development of a variety
of multiscale methods, including accelerated molecular dynamics,
kinetic Monte Carlo, phase field models, and diffusive molecular
dynamics.  In this talk, I will survey some of these approaches
and discuss common mathematical assumptions that underlie them
while also highlighting where approximations have been made.
Rigorous results will be presented, where available, along with
outstanding mathematical challenges.

Thu. 03/22, 1-2pm, TILT Auditorium 
Catherine Good
Host: Jess Ellis
(Postponed to Fall 2018, due to weather conditions in Northeast) 
Making Mindsets Matter: Classroom Cultures That Increase Student Engagement, Learning, and Achievement in Mathematics 
Abstract: I’m just not a math person!  How many times have you heard this statement as an excuse for students’ low performance in math?  But it conveys more than just an excuse... it also belies an underlying mindset about the nature of one’s math abilities.  And as research has shown, how students think about themselves as learners... their mindsets... have important implications for their motivation, learning, engagement and performance.  In this session, Dr. Good will share research on a variety of mindsets that shape students’ identities as learners.  These include beliefs about the nature of math intelligence, feelings of academic belonging, and purpose.

Mon. 02/12, 4-5pm, Weber 223
David Zureick-Brown, Emory University
Host: Rachel Pries
Title: Beyond Fermat's Last Theorem
Abstract: What do we (number theorists) do with ourselves now that Fermat's last theorem (FLT) has fallen?  I'll discuss lots of generalizations of FLT (and some underlying intuitions) --  for instance, for integers a,b,c >= 2 satisfying 1/a + 1/b + 1/c < 1, Darmon and Granville proved the single generalized Fermat equation x^a + y^b = z^c has only finitely many coprime integer solutions; conjecturally something stronger is true: for a,b,c \geq 3 there are no non-trivial solutions and for (a,b,c) = (2,3,n) with n >= 10 the only solutions are the trivial solutions and (+- 3,-2,1) $ (or (+-3,-2,+-1) $ when n is even).

Fall 2017: 

Mon., 11/13, 4-5pm, Weber 237
Hoon Hong, North Carolina State University
Host: Dan Bates
Title: "Root Separation Bound"
Abstract:  Let f be a square-free polynomial.  The root separation of f is the minimum of the pair-wise distance between the complex roots of f.  Finding a lower bound on the root separation is a fundamental problem, arising in numerous disciplines.  Due to its importance, there has been extensive research on this problem, resulting in various bounds.  In this talk, we present another bound, which is "nicer" than the previous bounds in that
(1) It is bigger (hence better) than the previous bounds.
(2) It is covariant under the scaling of the roots, unlike the previous bounds.
If time allows, we will also describe a generalization to multivariate polynomials systems.  This is a joint work with Aaron Herman and Elias Tsigaridas.

Mon. 11/13, 3-4pm, Weber 237
Joceline Lega, University of Arizona
Host: Patrick Shipman
Title: "A Three-pronged Approach to Predicting the Spread of Mosquito-borne Diseases"
Abstract:  Aedes aegypti is a mosquito that can transmit diseases like dengue, chikungunya, and Zika.  This talk will present a three-pronged approach to the modeling of Aedes aegypti-borne diseases, resulting from a collaboration with colleagues in the College of Public Health and in the School of Geography and Development at the University of Arizona.  Specifically, I will first discuss a mosquito abundance model that takes into account how meteorological data (temperature, precipitation, relative humidity) affect mosquito development and survival, and will describe its calibration against surveillance data in Puerto Rico.  Then, I will present a simple nonlinear growth model that is able to capture trends in disease incidence reports at the level of a country, and illustrate its efficacy in predicting the 2014-15 chikungunya epidemic in the Caribbean and the Americas.  Finally, I will show how a network-based approach that includes population flow between cities allows for a unified description of the spread of chikungunya and Zika in the small island nation of Dominica.  This talk will be accessible to a broad audience of scientists interested in the mathematical modeling of mosquito-borne diseases.

Mon. 10/16, 4-5pm, Weber 223
Martina Bukac, University of Notre Dame
Host James Liu
Title: "Interaction between a Fluid and Elastic and Poroelastic Materials with
Applications to Blood Flow"

Abstract: The interaction between a fluid, elastic structure, and poroelastic material
plays a fundamental role in many biomedical applications.  An example of such
application is the interaction between blood, arterial wall, and blood clot.  This
multi-physics problem features three different types of coupling: fluid-elastic structure
coupling, fluid-poroelastic material coupling, and elastic structure-poroelastic material
coupling, resulting in a fully coupled, non-linear, moving boundary problem.  As a
consequence, numerical algorithms that split the fluid dynamics, structure mechanics,
and poroelastic material dynamics are a natural choice.  We propose stable, partitioned
methods for the coupled problem.  We present numerical tests where we investigate
the effects of the material properties of the poroelastic medium on the fluid flow.  Our
findings indicate that the flow patterns highly depend on the storativity of the poroelastic

Mon. 09/25, 4-5pm, Weber 223 
Jason Cantarella, University of Georgia
Host Clayton Shonkwiler
Title: "The Differential Geometry of Spaces of Polygons and Polymers"
Abstract: We are interested in understanding the geometry of the Riemannian
manifold of space polygons.  Applications include the study of random walks
and polymers, linkages, and protein shapes.  We'll start with the geometry of
the space of open polygons in R^3, as this naturally models protein shapes. 
We identify this space with quaternionic projective space, and use the metric
on HP^n to cluster some protein shapes.  We will then turn to closed polygons,
where we use the natural symplectic structure of closed polygon space to
understand the distribution of point-to-point distances in the polygon and
construct a sampling algorithm.  To end the talk, we'll discuss some work
in progress on making the metric structure of closed polygon space more
easily visible by writing closed polygons as a quotient space (instead of
a subspace) of the open polygons.

Last modified by James Liu, Mon. 03/05/2018