Seminars and Colloquia by Series

Simplification of singularities of Lagrangian and Legendrian fronts

Series
Geometry Topology Seminar
Time
Monday, February 11, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Daniel Álvarez-Gavela – IAS
We will present an h-principle for the simplification of singularities of Lagrangian and Legendrian fronts. The h-principle says that if there is no homotopy theoretic obstruction to simplifying the singularities of tangency of a Lagrangian or Legendrian submanifold with respect to an ambient foliation by Lagrangian or Legendrian leaves, then the simplification can be achieved by means of a Hamiltonian isotopy. We will also discuss applications of the h-principle to symplectic and contact topology.

Convex-Nonconvex approach in segmentation and decomposition of scalar fields defined over triangulated surfaces

Series
Applied and Computational Mathematics Seminar
Time
Monday, February 11, 2019 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Martin Huska – University of bologna, Italy
In this talk, we will discuss some advantages of using non-convex penalty functions in variational regularization problems and how to handle them using the so-called Convex-Nonconvex approach. In particular, TV-like non-convex penalty terms will be presented for the problems in segmentation and additive decomposition of scalar functions defined over a 2-manifold embedded in \R^3. The parametrized regularization terms are equipped by a free scalar parameter that allows to tune their degree of non-convexity. Appropriate numerical schemes based on the Alternating Directions Methods of Multipliers procedure are proposed to solve the optimization problems.

Fun with Mac Lane valuations

Series
Algebra Seminar
Time
Monday, February 11, 2019 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Andrew Obus – Baruch College, CUNY –
Mac Lane's technique of "inductive valuations" is over 80 years old, but has only recently been used to attack problems about arithmetic surfaces. We will give an explicit, hands-on introduction to the theory, requiring little background beyond the definition of a non-archimedean valuation. We will then outline how this theory is helpful for resolving "weak wild" quotient singularities of arithmetic surfaces, as well as for proving conductor-discriminant inequalities for higher genus curves. The first project is joint work with Stefan Wewers, and the second is joint work with Padmavathi Srinivasan.

Singularities of Lagrangian and Legendrian fronts

Series
Geometry Topology Seminar Pre-talk
Time
Monday, February 11, 2019 - 12:45 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Daniel Álvarez-Gavela – IAS
The semi-cubical cusp which is formed in the bottom of a mug when you shine a light on it is an everyday example of a caustic. In this talk we will become familiar with the singularities of Lagrangian and Legendrian fronts, also known as caustics in the mathematics literature, which have played an important role in symplectic and contact topology since the work of Arnold and his collaborators. For this purpose we will discuss some basic singularity theory, the method of generating families in cotangent bundles, the geometry of the front projection, the Legendrian Reidemeister theorem, and draw many pictures of the simplest examples.

Hamiltonian Cycles in Uniform Hypergraphs with Large Minimum Degree

Series
Combinatorics Seminar
Time
Friday, February 8, 2019 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Andrzej Rucinski – Emory and AMU Poznań

Abstract: Reiher, Rödl, Ruciński, Schacht, and Szemerédi proved, via a modification of the absorbing method, that every 3-uniform $n$-vertex hypergraph, $n$ large, with minimum vertex degree at least $(5/9+\alpha)n^2/2$ contains a tight Hamiltonian cycle. Recently, owing to a further modification of the method, the same group of authors joined by Bjarne Schuelke, extended this result to 4-uniform hypergraphs with minimum pair degree at least, again, $(5/9+\alpha)n^2/2$. In my talk I will outline these proofs and point to the crucial ideas behind both modifications of the absorbing method.

Travel Behavior Modeling Using Machine Learning

Series
ACO Student Seminar
Time
Friday, February 8, 2019 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Xilei Zhao – ISyE, Georgia Tech –

The popularity of machine learning is increasingly growing in transportation, with applications ranging from traffic engineering to travel demand forecasting and pavement material modeling, to name just a few. Researchers often find that machine learning achieves higher predictive accuracy compared to traditional methods. However, many machine-learning methods are often viewed as “black-box” models, lacking interpretability for decision making. As a result, increased attention is being devoted to the interpretability of machine-learning results.

In this talk, I introduce the application of machine learning to study travel behavior, covering both mode prediction and behavioral interpretation. I first discuss the key differences between machine learning and logit models in modeling travel mode choice, focusing on model development, evaluation, and interpretation. Next, I apply the existing machine-learning interpretation tools and also propose two new model-agnostic interpretation tools to examine behavioral heterogeneity. Lastly, I show the potential of using machine learning as an exploratory tool to tune the utility functions of logit models.

I illustrate these ideas by examining stated-preference travel survey data for a new mobility-on-demand transit system that integrates fixed-route buses and on-demand shuttles. The results show that the best-performing machine-learning classifier results in higher predictive accuracy than logit models as well as comparable behavioral outputs. In addition, results obtained from model-agnostic interpretation tools show that certain machine-learning models (e.g. boosting trees) can readily account for individual heterogeneity and generate valuable behavioral insights on different population segments. Moreover, I show that interpretable machine learning can be applied to tune the utility functions of logit models (e.g. specifying nonlinearities) and to enhance their model performance. In turn, these findings can be used to inform the design of new mobility services and transportation policies.

Convex Relaxation for Multimarginal Optimal Transport in Density Functional Theory

Series
Applied and Computational Mathematics Seminar
Time
Friday, February 8, 2019 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Lexing Ying – Stanford University

Please Note: We will go to lunch together after the talk with the graduate students.

We introduce methods from convex optimization to solve the multi-marginal transport type problems arise in the context of density functional theory. Convex relaxations are used to provide outer approximation to the set of N-representable 2-marginals and 3-marginals, which in turn provide lower bounds to the energy. We further propose rounding schemes to obtain upper bound to the energy.

Compactifying parameter spaces

Series
Intersection Theory Seminar
Time
Thursday, February 7, 2019 - 15:18 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Tianyi Zhang – Georgia Tech
We continue the discussion of Chapter 8 in 3264 and All That. We will discuss complete quadrics, Hilbert schemes and Kontsevich spaces.

Homogenization of a class of one-dimensional nonconvex viscous Hamilton-Jacobi equations with random potential

Series
Stochastics Seminar
Time
Thursday, February 7, 2019 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Atilla Yilmaz – Temple University –
I will present joint work with Elena Kosygina and Ofer Zeitouni in which we prove the homogenization of a class of one-dimensional viscous Hamilton-Jacobi equations with random Hamiltonians that are nonconvex in the gradient variable. Due to the special form of the Hamiltonians, the solutions of these PDEs with linear initial conditions have representations involving exponential expectations of controlled Brownian motion in a random potential. The effective Hamiltonian is the asymptotic rate of growth of these exponential expectations as time goes to infinity and is explicit in terms of the tilted free energy of (uncontrolled) Brownian motion in a random potential. The proof involves large deviations, construction of correctors which lead to exponential martingales, and identification of asymptotically optimal policies.

Interpolative decomposition and its applications

Series
School of Mathematics Colloquium
Time
Thursday, February 7, 2019 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Prof. Lexing Ying – Stanford University
Interpolative decomposition is a simple and yet powerful tool for approximating low-rank matrices. After discussing the theory and algorithms, I will present a few new applications of interpolative decomposition in numerical partial differential equations, quantum chemistry, and machine learning.

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