2018-2019 Colloquia
Title: On the tangent Lie group of a symplectic Lie group
Date: Wednesday, May 8th, 2019
Time: 12:30—1:30pm
Room: S-213
Speaker: Dr. David Pham at (QCC)
Refreshments will be served
Abstract
A symplectic Lie group is a Lie group with a left-invariant symplectic form. Since the tangent bundle of any Lie group is itself a Lie group (the so-called tangent Lie group), it is natural to ask if the tangent Lie group of a symplectic Lie group is also a symplectic Lie group. In this talk, I discuss recent work where I show that this is indeed the case. Specifically, I show that for a symplectic Lie group G, one can construct a left-invariant symplectic form on the tangent Lie group TG using vertical and complete lifts of left-invariant vector fields on G. This construction is motivated by the work of Asgari and Salimi Moghaddam who studied left-invariant Riemannian metrics on TG that were constructed using vertical and complete lifts of left-invariant vector fields on G. Hence, the present construction can be viewed as the symplectic analogue of this. A nice upshot of this construction is that by starting with a non-abelian symplectic Lie group, one can generate non-abelian symplectic Lie groups of arbitrarily high dimension by taking iterated tangent bundles.
Title: Real inflection points on real (hyper)elliptic curves
Date: Wednesday, April 10th, 2019
Time: 12:30—1:30pm
Room: S-213
Speaker: Dr. Ethan Cotterill at (Boston College)
Refreshments will be served
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.
Title: Binomial arrays and generalized Vandermonde identities
Date: Wednesday, March 27th, 2019
Time: 12:10—1:10pm
Room: S-213
Speaker: Dr. Robert Donley at (QCC)
Refreshments will be served
Abstract
"It is not exaggerated to say the Catalan numbers are the most prominent sequence in combinatorics." (Kauers and Paule, 2013) Associated to the Catalan numbers is an evolving set of numerical triangles, for which we suggest perhaps a final form. These triangles belong to a larger class of arrays with features of both the extended Pascal's triangle and Riordan arrays. We introduce the notions of generalized binomial transform and binomial array, and we describe several hockey stick rules (3 short, 6 long) and a visual interpretation of Vandermonde's identity/convolution for these arrays. Finally, we obtain two families of sequences generalizing the Catalan numbers mostly absent from the OEIS.
Title: Midsemester Presentations of Student Research
Date: Wednesday, March 27th, 2019
Time: 1:10—2:00pm
Room: S-213
Abstract
Title: Exotic four-manifolds via positive factorizations
Date: Wednesday, March 13th, 2019
Time: 1:00—2:00pm
Room: S-322
Speaker: Dr. Refik Inanc Baykur at (University of Massachusetts Amherst)
Abstract
We will discuss new ideas and techniques for producing positive Dehn twist factorizations of surface mapping classes, which yield novel constructions of many interesting four-manifolds, such as symplectic Calabi-Yau surfaces and exotic rational surfaces, via Lefschetz pencils.
Title: Asymptotic enslavement in hydrodynamic equations and applications to data assimilation
Date: Wednesday, February 27th, 2019
Time: 12:00—1:00pm
Room: S-213
Speaker: Dr. Vincent R Martinez at (Hunter College)
Refreshments will be served
Abstract
In their 1967 seminal paper, Foias and Prodi captured a notion of finitely many degrees of freedom in the context of the two-dimensional (2D) incompressible Navier-Stokes equations (NSE). In particular, they proved that if a sufficiently large low-pass filter of the difference of two solutions converge to 0 asymptotically in time, then the corresponding high-pass filter of their difference must also converge to 0 in the long-time limit. In other words, the high modes are “eventually enslaved” by the low modes. One could thus define the number of degrees of freedom to be the smallest number of modes needed to guarantee this convergence for a given flow. This property has since led to several developments in the long-time behavior of solutions to the NSE, particularly to the mathematics of turbulence, but more recently to data assimilation. In this talk, we will give a survey of rigorous studies made for a certain approach to data assimilation that exploits this asymptotic coupling property as a feedback control. We will discuss these issues in the specific context of the 2D NSE, as well as a geophysical equation called the 2D surface quasi-geostrophic equation.
Title: On a Stochastic Logistic Growth Model with Predation: Dynamics and Optimal Harvesting
Date: Wednesday, February 13th, 2019
Time: 12:30pm—1:30pm
Room: S-213
Speaker: Dr. Susana Couto Pinheiro at (QCC)
Refreshments will be served
Abstract
Stochastic differential equations have a wide variety of applications, ranging from population dynamics to problems arising from finance and actuarial science. In this talk, I will discuss how stochastic differential equations and optimal control can be employed to gain additional insight into the growth of a population. More precisely, given a logistic growth model with a predation term and a stochastic perturbation given by a diffusive term with a power-type coefficient, I will provide a qualitative characterization for its asymptotic behavior. Additionally, I will also discuss an application to optimal management of resources. Namely, I will consider a real asset such as, for instance, a farm or an aquaculture facility, devoted to the exploration of a unique population whose growth follows a stochastic differential equation such as described above, and look for the optimal harvesting strategy associated with such culture or population.
Title: Short Introduction to Fractional Calculus
Date: Wednesday, November 28th, 2018
Time: 1:00pm—2:00pm
Room: S-213
Speaker: Dr. Lyubomir Boyadzhiev at (QCC)
Refreshments will be served
Abstract
In the last three decades the Fractional Calculus (differentiation and integration of arbitrary order) became one of the most intensively developing branches of the mathematical analysis due to its numerous applications in physics, chemistry, biology and engineering.
An introductory view on the mathematical aspects of the Fractional Calculus will be presentedin this talk. The Riemann- Liouville fractional integral and the Caputo fractional derivative will be defined and some of their properties discussed. The focus of the talk ison the join application of the Laplace and Fourier integral transforms for solving the Fractional Schrödinger equation.
Title: An Elementary Introduction to the Langlands Program and Local Factors
Date: Wednesday, November 21st, 2018
Time: 1:00pm—2:00pm
Room: S-213
Speaker: Dr. Yusuf Danisman at (QCC)
Refreshments will be served
Abstract
Langlands program reveals the deep links between number theory and harmonic analysis and it roughly states that the L-functions arising in number theory are special realization of L-functions of automorphic representations. These objects are global and by local-global principle, such objects can be analyzed purely locally. This is one of the motivations to study local representation theory.
One of the conjectures in the Langlands program called local Langlands conjecture predicts a connection between representation theory of p-adic groups with the representation theory of the Galois group of p-adic fields. Therefore it is a non-abelian generalization of abelian local class field theory.
In this talk, I will give an overview of the Langlands program, the local Langlands conjecture for GL(2) and some recent results about computation of local factors.
Title: Verification of Polynomial Interrupt Timed Automata
Date: Wednesday, November 14th, 2018
Time: 1:00pm—2:00pm
Room: S-213
Speaker: Dr. Mathieu Sassolas at (QCC)
Refreshments will be served
Abstract
Modeling real world systems implies taking into account the continuous elapsing of time along with the discrete set of states the system can operate in, thus yielding so called /hybrid systems/. However, verification of such systems is mostly undecidable, and finding decidable fragments has been an ongoing research topic for the last 25 years. In this work we propose a decidable model of hybrid systems taking into account constraints expressed by polynomials instead of the more widespread linear constraints. The decision procedure relies on the cylindrical decomposition of reals.
This talk is based on joint work with Béatrice Bérard, Serge Haddad, Claudine Picaronny, and Mohab Safey El Din.
Midsemester Presentations of Student Research
Date: Wednesday, October 31st, 2018
Time: 12:10—2:00pm
Room: S-213
Refreshments will be served
Online Schedule (subject to change):
https://docs.google.com/spreadsheets/d/1LfVqFbk_0YSJ86LFDiNM41wQYjs4fm0VUV8MhqoZZzs/edit?usp=sharing
Title: Operator theory in Drury-Arveson space
Date: Wednesday, October 24th, 2018
Time: 1:00pm—2:00pm
Room: S-213
Speaker: Dr. QuanLei Fang at (Bronx Community College-CUNY)
Refreshments will be served
Abstract
The Drury-Arveson Space, as a Hilbert function space, plays an important role in multivariable operator theory. It also has the structure of a Hilbert module given by a commuting tuple of operators acting on it. In this talk I will discuss some analytical aspects of this space.
Title: Extreme-scale Methods for Content-based Image Retrieval in Histopathology
Date: Wednesday, October 17th, 2018
Time: 12:30pm—1:30pm
Room: S-213
Speaker: Dr. Esma Yildirim at (QCC)
Refreshments will be served
Abstract
Whole slide images (WSIs) are very large (30-50GB each in uncompressed format), multiple resolution images produced by whole slide scanners and are widely used by pathology departments for diagnostic, educational and research purposes. Content-based image retrieval (CBIR) applications allow pathologists to perform a sub-region search to automatically identify image patterns that are consistent with a given query patch with cancerous tissue patterns. The results can then be used to draw comparisons among patient samples in order to make informed decisions regarding likely prognoses and most appropriate treatment regimens. In today’s technology, a whole slide scanner is able to produce around 400 images in under 3 minutes resulting in an avalanche of big data which requires extreme-scale computing algorithms and methodologies for CBIR applications to search for cancerous patterns. In this talk, challenges of big, unstructured WSI data will be defined; novel, extremely scalable data access methods for a developed CBIR workflow will be presented and performance results will be given comparing 3 different access scenarios to improve the overall time for searching large WSI datasets: Parallel file system access, distributed memory staging and deep memory hierarchies using solid-state drives(SSDs).
Title: Dimensions of Spaces of Paramodular Forms
Date: Wednesday, October 10th, 2018
Time: 12:30pm—1:30pm
Room: S-213
Speaker: Dr. Jeffery Breeding Allison (Data Scientist at Macy's)
Refreshments will be served
Abstract
Title: Annulus Type Asymptotic Plateau Problem in Hyperbolic Three Space
Date: Wednesday, September 26th, 2018
Time: 1:00pm—2:00pm
Room: S-213
Speaker: Dr. Biao Wang at (QCC)
Refreshments will be served
Abstract
In this talk, I will introduce the concept of hyperbolic space and minimal catenoids (i.e. the minimal surfaces which are surfaces of revolution). Then I will talk about how to use minimal catenoids to solve the annulus type asymptotic Plateau problem in hyperbolic three space under some assumptions.
Title: Multiplier ideals of analytically irreducible plane curves
Date: Thursday, July 11th, 2019
Time: 10:00—11:00am
Room: S-223
Speaker: Mingyi Zhang (Northwestern)
Abstract
Multiplier ideals and their vanishing theorems are very useful in birational geometry, but it is usually hard to compute explicitly. I will give an explicit formula for multiplier ideals of analytically irreducible plane curves.
