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Lorena Bociu, NC State, Fluid Flows through Deformable Porous Media: Analysis and Applications to Ocular Perfusion

SAS 4201

Modeling of fluid flows through porous deformable media is relevant for many applications in biology, medicine and bioengineering, including blood flow through human tissues and fluid flow inside cartilages and bones. These fluid-structure mixtures are described mathematically by nonlinear poro-visco-elastic systems in bounded domains, with mixed boundary conditions. In this talk, I will present well-posedness…

Joey Hart, NC State, SIAM Tutorial Series: Introduction to Monte Carlo Methods

SAS 1218

In this lecture we will present basis theoretical and algorithmic properties of Monte Carlo methods. In particular, their convergence properties and implementational simplicity will be highlighted. There are a variety of Monte Carlo methods but we will focus on two, namely, Monte Carlo integration and Markov Chain Monte Carlo. Prior knowledge of Monte Carlo methods…

Tye Lidman, NC State, Band surgeries and lens space surgeries

SAS 4201

Dehn surgery is a fundamental operation in three-manifold topology which turns a knot into a new three-manifold. We characterize Dehn surgeries between certain lens spaces and relate this to an elementary question in knot theory. This is joint work with Allison Moore.

What Is?

Lie Algebras, manifolds, varieties. We have all heard terms like these, but may not know quite what they mean. This week we will have introductory "What Is?" talks. These talks are intended to build your vocabulary/intuition for future talks. This week we will hear about: Lie Algebras, Leibniz Algebras, Representations, Algebraic Varieties.

Richard Rimanyi, UNC Chapel Hill, Counting partitions and quantum dilogarithm identities

SAS 4201

In the theory of Donaldson-Thomas invariants for quivers one finds identities for quantum dilogarithm series. The combinatorial interpretation of the simplest of these identities is equivalent to a clever way of counting partitions. The combinatorial interpretation of more involved dilogarithm identities is not known. In the talk we will explore the geometry (DT invariants), topology…

Nik Bravo, Data-Driven Model Development and Feedback Control Design for PZT Bimorph Actuators and Lider Leon, Parameter and Active Subspace Analysis for a Polydomain Ferroelectric Phase Field Model

SAS 4201

Nik Bravo: Title: Data-Driven Model Development and Feedback Control Design for PZT Bimorph Actuators Abstract: In the talk, we discuss the development of a high-fidelity and surrogate model for a PZT bimorph used as an actuator for micro-air vehicles including Robobee. The models must quantify the nonlinear, hysteretic, and rate-dependent behavior inherent to PZT in…

Xiao Bao Lin, NC State, Chaotic Traveling Wave Solutions In Coupled Circuits

SAS 4201

Coupled array of Chua's circuits has been studied for many years. Some experimental and numerical study of traveling waves were conducted by Perez and Chua in 1993. Existence of periodic traveling waves were proved by S.-N. Chow, M. Jiang and X.-B. Lin in 2013. This talk is based on a joint work with F. Geng…

Adam Levine, Duke, Heegaard Floer invariants for homology $S^1 \times S^3$s

SAS 4201

Using Heegaard Floer homology, we construct a numerical invariant for any smooth, oriented 4-manifold X with the homology of $S^1 \times S^3$. Specifically, we show that for any smoothly embedded 3-manifold Y representing a generator of H_3(X), a suitable version of the Heegaard Floer d invariant of Y, defined using twisted coefficients, is a diffeomorphism…

Davis Atkinson, Graham Pash, and Jaye Sudweeks, Modeling the New Jersey Turnpike in 99 Hours

“When am I going to use this?”      It’s a question every student has asked at least once. The Modeling Contest in Mathematics (MCM), held annually by COMAP, provides a way for undergraduates to apply the knowledge gained from classes to real world problems. Each year, COMAP presents six interesting prompts on anything ranging…

Hamid Krim, SIAM Student Chapter Data Science Lecture Series: Convexity, Sparsity, Nullity and all that in Machine Learning

Daniels 322

High dimensional data exhibit distinct properties compared to its low dimensional counterpart; this causes a common performance decrease and a formidable computational cost increase of traditional approaches. Novel methodologies are therefore needed to characterize data in high dimensional spaces. Considering the parsimonious degrees of freedom of high dimensional data compared to its dimensionality, we study…

Math Doesn’t Bug Me

11 West Jones Street, Raleigh, NC, 27601, United States

Discover the beauty of mathematics and its wide applicability in everyday life. Enjoy math games and poster presentations, and interact with NCSU mathematicians  

Leonardo Mihalcea, Chern-Schwartz-MacPherson classes for Schubert cells: geometry and representation theory

SAS 4201

A compact manifold has a tangent bundle, and a natural question is to find a replacement for the Chern classes of the tangent bundle, in the case when the space is singular. The Chern-Schwartz-MacPherson (CSM) classes are homology classes which ``behave like" the Chern classes of the tangent bundle, and are determined by a functoriality…

Shu-Cherng Fang, NC State ISE, Linear Reformulation of Polynomial Discrete Programming for Fast Computation

SAS 4201

Optimization models involving a polynomial objective function and multiple polynomial constraints with discrete variables are often encountered in engineering, management and systems. Treating the non-convex cross-product terms is the key. State-of- the-art methods usually convert such a problem into a 0-1 mixed integer linear programming problem, and, then adopt a branch-and- bound scheme to find…

Erdal Imamoglu, NC State, Algorithms for Solving Linear Differential Equations with Rational Function Coefficients

SAS 4201

We present two algorithms for computing hypergeometric solutions of a second order linear differential equation with rational function coefficients. Our first algorithm uses quotients of formal solutions, modular reduction, Hensel lifting, and rational reconstruction. Our second algorithm first tries to simplify the input differential equation using integral bases and then uses quotients of formal solutions.

What Is?

Juanita Pinzon-Caicedo, NC State, Crunched Charms: A Short Intro to Knot Theory

Knot theory is the subarea of topology that studies math- ematical knots or different ways of placing a circle inside 3- dimensional space. Proving that two knots are distinct (or equivalent) is the main problem knot theorists deal with. In the talk, we will discuss methods used to distinguish knots. For a simple introduction click…

Amy Ward, University of Southern California, Scheduling in a Many-Server, Multi-Class System: The Impact of the Customer Patience Distribution

Withers 232A

The study of scheduling problems has a long history in the academic literature.  However, many classic models used to study scheduling problems do not incorporate customer impatience.  Furthermore, many of the ones that do assume the time a customer is willing to wait for service is exponentially distributed.  The issue is that that assumption can…