Past Year Events of the Week

Week of March 27 - March 31, 2017

*Friday, March 31*

**Topic**

*Thursday, March 30*

**Topic**

*Thursday, March 30*

**Topic**

*Wednesday, March 29*

**Topic**

*Tuesday, March 28*

**Topic**

*Monday, March 27*

**Topic**

Week of March 24 - March 20, 2017

*Friday, March 24*

**Topic**

*Thursday, March 23*

## Colloquium

**Nonuniqueness of weak solutions to the SQG equation**

*Thursday, March 23*

## Algebra & Combinatoric seminar

**Points, symbolic powers and a conjecture by G. V. Chudnovsky.**

*Wednesday, March 22*

## Probability and Statistics

**Long and medium time behavior of stochastically modeled biochemical reaction networks**

In this talk, I will focus on stochastic models of biochemical reaction systems and discuss two topics. In the first, I will provide a large class of interesting nonlinear models for which the stationary distribution can be solved for explicitly. Such results are particularly useful for averaging purposes in multi-scale settings. The second topic will pertain to an interesting class of models that exhibits fundamentally different long-term behavior when modeled deterministically or stochastically (the ODEs predict stability, the stochastic model goes extinct with probability one). Recent work pertaining to the distribution of the stochastic model on compact time intervals (similar to the study of the quasi-stationary distribution) resolves the apparent discrepancy between the modeling choices.

*Tuesday, March 21*

**Thermal Stratification in Geophysical Fluid Flows**

**Location: Dinwiddie Hall**

*Tuesday, March 21*

## Student Colloquium

**Useful Result for Regularity of Edge Ideals**

Joseph Skelton - Tulane University

*Monday, March 20*

**Topic**

Week of March 18 - March 13, 2017

*Saturday, March 18*

## SCALA

*Friday, March 17*

## SCALA

*Thursday, March 16*

**Topic**

*Thursday, March 16*

## Colloquium

**Non-Archimedean analytic curves in algebraic varieties**

*Wednesday, March 15*

## Probability and Statistics (Joint with Applied Math)

**Asymptotic analysis for randomly forced magnetohydrodynamics**

Susan Friedlander - University of Southern California

*Tuesday, March 14*

## Graduate Student Colloquium

**Everything You Always Wanted to Know About Pi (But Were Afraid to Ask)**

*Monday, March 13*

## Probability and Statistics (Special Day)

**Transition probabilities for degenerate diffusions arinsing in population genetics**

**Week of March 10 - March 6, 201**7

*Friday, March 10*

**Topic**

*Thursday,* *March* 9

**The sound of silence — Recovering signals from time-frequency zeros**

Disentangling multicomponent nonstationary signals into coherent AM-FM modes is usually achieved by identifying « loud » time-frequency trajectories where energy is locally maximum. We will here present an alternative perspective that relies on « silent » points, namely spectrogram zeros. Based on the theory of Gaussian analytic functions, a number of results will be presented regarding the distribution of such zeros considered as a point process in the plane, with repulsive properties. The rationale and the implementation of the zeros-based approach for recovering signals embedded in noise will then be discussed, with an application to the extraction and characterization of actual gravitational wave chirps.

*Thursday,* *March 9*

**A DYNAMIC BUCHBERGER ALGORITHM**

*Wednesday, March 8*

**Simulating the Mean Efficiently and to a Given Tolerance**

*Monday, March 7*

**Topic**

*Tuesday, March 7*

## Tulane AWM/AMS Student Chapters present:

**Applications of computational geometry and topology in shape matching**

Abstract: In this talk we will discuss approaches of computational geometry and topology to theory and applications of geometric shape matching. This includes the Frechet distance for curves, the use of persistent homology, and applications in map construction and comparison.

*Monday, March 6*

**Topic**

Week of March 3 - February 27, 2017

*Friday, March 3*

**Topic**

*Thursday, March 2*

## Algebra & Combinatorics

**The depth function of ideals in polynomial rings.**

*Thursday, March 2*

**Topic**

*Wednesday, February 1*

**Topic**

*Tuesday, February 28*

**Mardi Gras Break**

All University Offices will be closed

Have a safe Holiday

*Monday, February 27*

**Mardi Gras Break**

All University Offices will be closed

Have a safe Holiday

**Week of February 24 - February 20, 2017**

*Friday, February 24*

**Topic**

*Thursday, February 23*

## Colloquium

**Why is the ergodic theory of stochastic PDEs different?**

*Thursday, February 23*

**Topic**

*Wednesday, February 22*

**Topic**

*Tuesday, February 21*

**Secret Meeting of the L5 Society**

*Monday, February 20*

**Topic**

**Week of February 17 - February 13, 2017**

*Friday, February 17*

**Topic**

*Thursday, February 16*

## Algebra and Combinatorics Seminar

**Classification of spherical diagonal actions of reductive groups, Part II.**

*Wednesday, February 15*

**Continuum approximation of invasion probabilities for stochastic population models**

In this talk, we compare popular continuum approximations for the invasion probability to its exact solution. In particular, methods known as "Diffusion (or Stochastic Differential Equation) Approximation" and "Exponential Approximation" are derived. We find analytical expressions for these approximations in the large population limit and then use numerical methods to evaluate the performance of the approximation methods for finite populations. Interestingly we find that the diffusion approximation fails to obtain the correct large population limit, but can perform well for small populations that experience near critical dynamics. The exponential approximation obtains the right large population limit in the supercritical regime, but fails to capture nonmontonic characteristics of the invasion probability for small to intermediate sized populations.

*Wednesday, February 14*

## GRAD STUDENT COLLOQUIUM

**Lasso, Group Lasso, and SLOPE**

From linear regression, I will introduce the penalty method such as ridge method and lasso method. However, in some cases, the variates have strong correlation with each other, then we can use the group lasso. After that, I will talk about SLOPE(sorted L-One Penalty Estimation), which is method similar to the lasso method and consider the false discovery rate as the criteria.

*Tuesday, February 14*

## COFFEE AND DISCUSSION: “Finding opportunities for conferences, workshops, etc”

**Location: Dinwiddie Hall 102**

*Monday, February 13*

## Special Mathematical Biology seminar

**Diabetes: One Disease, Many Paths**

**Week of February 10 - February 6, 2017**

*Friday, February 10*

**Topic**

*Thursday, February 9*

## Colloquium

**Global Regularity v.s. Finite Time Blowup for Compressible Euler Equations**

*Wednesday, February 9*

## Algebra and Combinatorics Seminar

**Classification of spherical diagonal actions of reductive groups**

*Wednesday, February 8*

## Probability and Statistics

**Scalings and saturation in infinite-dimensional control problems with applications to stochastic partial differential equations.**

*Tuesday, February 7*

## Graduate Student Colloquium

**Poincare Duality With Local Coecients**

*Monday, February 7*

## TULANE AWM/AMS STUDENT CHAPTERS

**Introduction to Riemannian Geometry**

*Monday, February 6*

**Topic**

Week of February 3 - January 30, 2017

*Friday, February 3*

**Topic**

*Thursday, February 2*

## Colloquium

**Limit Shapes for Rational Functions**

Robin PemantleUniversity of Pennsylvania (host mahir can)

**Time: 3:30**

*Thursday, February 2*

## Algebra and Combinatorics Seminar

**Introduction to the Hodge Conjecture (part 2)**

*Wednesday, February 1*

**Topic**

*Friday, February 31*

## Graduate Student Colloquium

**Some algebraic properties of toric edge rings**

*Tuesday, January 31*

## AWM / AMS

**Biofluids of reproduction: oscillators, viscoelastic networks and sticky situations.**

*Monday, January 30*

**Topic**

**Week of January 27 - January 23, 2017**

*Friday, January 27*

**Topic**

*Thursday, January 26*

## Algebra and Combinatorics Seminar

**Introduction to the Hodge Conjecture**

*Wednesday, January 25*

**Topic**

*Tuesday, January 24*

## Graduate Student Colloquium

**The Method of Brackets**

*Monday, January 23*

**Topic**

**Week of January 20 - January 16, 2017**

*Friday, January 20*

**Topic**

*Thursday, January 20*

**Sixth Annual Winter Workshop on Neuromechanics and Dynamics of Locomotion**

Location: Lavin Bernick Center for University Life (building 29) - Kendall Cram Room

*Thursday, January 19*

**Sixth Annual Winter Workshop on Neuromechanics and Dynamics of Locomotion**

Location: Lavin Bernick Center for University Life (building 29) - Kendall Cram Room

*Thursday, January 19*

**Topic**

*Wednesday, January 18*

**Topic**

*Tuesday, January 17*

**Topic**

*Monday, January 16*

**Martin Luther King Day**

Week of March 27 - March 31, 2017

**Speaker - Institution
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**Abstract:
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**Location:
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**Time:**

**Speaker - Institution
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**Time:**

**Speaker - Institution
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**Location:
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**Time:**

**Speaker - Institution
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**Location:
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**Time:**

**Speaker - Institution
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**Location:
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**Time:**

Week of March 24 - March 20, 2017

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Vlad Vicol - Princeton (Host Nathan Glatt-Holtz)
**

**Abstract:
**

**Location: Dinwiddie 102
**

**Time: 3:30**

**Paolo Mantero - University of Arkansas
**

**Abstract:
**

What is the smallest possible degree of an equation passing at least m times through t given points in the complex projective space P^N? The answer is not known (except in few special cases), however the complex analyst G. V. Chudnovsky in 1979 conjectured a lower bound, which until last year was only known to hold for points in P^2, general points in P^3 and certain extremal configurations in P^N.

In this talk we will survey the evolving framework of conjectures and results around the above question, and prove Chudnovsky's conjecture for any set of very general points in P^N.

**Location: Gibson Hall 400A
**

**Time: 12:45**

**David Anderson - University of Wisconsin
**

**Abstract:
**

In this talk, I will focus on stochastic models of biochemical reaction systems and discuss two topics. In the first, I will provide a large class of interesting nonlinear models for which the stationary distribution can be solved for explicitly. Such results are particularly useful for averaging purposes in multi-scale settings. The second topic will pertain to an interesting class of models that exhibits fundamentally different long-term behavior when modeled deterministically or stochastically (the ODEs predict stability, the stochastic model goes extinct with probability one). Recent work pertaining to the distribution of the stochastic model on compact time intervals (similar to the study of the quasi-stationary distribution) resolves the apparent discrepancy between the modeling choices.

**Location: Gibson 126
**

**Time: 3:00**

**Speaker - Institution
**

**Abstract:
**

**Time: 2:00**

Joseph Skelton - Tulane University

Abstract:

The talk will cover fundamental definitions relating to the regularity of edge ideals, as well as cover a useful result for the bounds of regularity.

**Location: Stanley Thomas 316
**

**Time: 4:15**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

Week of March 18 - March 13, 2017

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Prof. William Cherry - University** **of North Texas (Host: Tai Ha)
**

**Abstract:
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Location: Dinwiddie 102

**Time: 3:30**

Susan Friedlander - University of Southern California

**Abstract:
**

**Location: Gibson 126
**

**Time: 3:00**

**Aram Bingham - Tulane University
**

**Abstract:
**

Imagine all of the internet burns down, with all the books inside it, and we have to recreate the current state of mathematics with our bare brains. What facts about pi (pronounced pee) will we retain? After reciting some of the trivia which is Pi Day orthodoxy, we will discuss proofs of those aspects of pi we take most for granted, making reference to open problems as well.

**Location: Stanley Thomas 316
**

**Time: 4:15**

**Camelia Pop - University of Minnesota (Host Scott McKinley)
**

**Abstract:
**

We provide a detailed description of the structure of the transition probabilities and of the hitting distributions of boundary components of a manifold with corners for a degenerate strong Markov process arising in population genetics. The Markov processes that we study are a generalization of the classical Wright-Fisher process. The main ingredients in our proofs are based on the analysis of the regularity properties of solutions to a forward Kolmogorov equation defined on a compact manifold with corners, which is degenerate in the sense that it is not strictly elliptic and the coefficients of the first order drift term have mild logarithmic singularities. This is joint work with Charles Epstein.

**Location: Stanley Thomas 316
**

**Time: 4:00**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Patrick Flandrin**CNRS and ENS-Lyon (host: Didier Gustavo)

**Abstract:
**

Disentangling multicomponent nonstationary signals into coherent AM-FM modes is usually achieved by identifying « loud » time-frequency trajectories where energy is locally maximum. We will here present an alternative perspective that relies on « silent » points, namely spectrogram zeros. Based on the theory of Gaussian analytic functions, a number of results will be presented regarding the distribution of such zeros considered as a point process in the plane, with repulsive properties. The rationale and the implementation of the zeros-based approach for recovering signals embedded in noise will then be discussed, with an application to the extraction and characterization of actual gravitational wave chirps.

**Location:** **Dinwiddie 102**

**Time: 3:30**

**John Perry | University of Southern Mississippi
**

**Abstract:
**

Gröbner bases are a major tool in commutative algebra, typically computed using the Buchberger algorithm. This algorithm is “static” in that it works with a fixed term ordering, required as input along with the ideal’s generators. In many cases, however, a “dynamic” Buchberger algorithm is more appropriate: it requires only the generators as input, and returns both a basis and an ordering that guarantees the Gröbner property. It computes the ordering by the guidance of a criterion inspired by an invariant of an ideal. This talk describes the algorithm, the traditional criterion to guide computation, and a new criterion.

**Location: Gibson Hall 400A
**

**Time: 12:45**

**Fred Hickernell** - Illinois Institute of Technology (HOST James Hyman)

**Abstract:
**

Various application problems are formulated as means of random variables, e.g., option pricing, multivariate probabilities, and Sobol' indices. When the distribution of the random variable is complicated, computer simulation can be used to approximate the population mean by a sample mean. Two big questions are how to draw the sample to minimize error, and what sample size is needed to guarantee the desired accuracy. This talk describes our best answers so far. The sampling error can be decomposed into a product of three factors.

One of these factors, the discrepancy, describes the efficiency of simulation. By assuming that the distribution of the random variable is nice, in some mathematically precise way, we can rigorously bound the error of the simulation and thus determined the sample size required.

**Location: Gibson 126
**

**Time: 3:00**

**Diego Villamizar - Tulane University
**

**Abstract:
**

I will talk about r-indecomposable factorial numbers, and how I do not know anything about them.

**Location: Stanley Thomas 316
**

**Time: 4:15**

**Dr Carola Wenk - Tulane University
**

**Abstract:
**

Abstract: In this talk we will discuss approaches of computational geometry and topology to theory and applications of geometric shape matching. This includes the Frechet distance for curves, the use of persistent homology, and applications in map construction and comparison.

**Location: Dinwiddie 102
**

**Time: 2:00**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

Week of March 3 - February 27, 2017

**Speaker - Institution
**

**Abstract:
**

**Location:
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**Time:**

**Tai Huy Ha - Tulane University
**

**Abstract:
**

We shall discuss what could be the depth function of an ideal in a polynomial ring. That is, for which function f(n), there exists an ideal I in a polynomial ring R such that depth R/I^n = f(n) for all n > 0.

**Location: Gibson 400A**

**Time: 12:45**

**Speaker - Institution
**

**Abstract:
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**Location:
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**Time:**

**Speaker - Institution
**

**Abstract:
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**Location:
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**Time:**

All University Offices will be closed

Have a safe Holiday

All University Offices will be closed

Have a safe Holiday

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Jonathan Mattingly - Duke (HOST: Nathan Glatt-Holtz and Scott McKinley)
**

**Abstract:
**

Ergodicity is one of the fundamental questions for a stochastic dynamical system, ensuring the convergence of long time averages of observable quantities to a statistical steady state independent of the initial condition.

I will explore why the ergodic theory of stochastic PDEs is different and how it underlines the basic difference between ODEs and PDEs. I will start at the beginning giving a crash course on the basic elements needed to prove an ergodic result. We will come to understand why sometimes ergodicity can be easy for hard PDEs. Time permitting I will touch on hypoellipticity in infinite dimensions and singular PDEs.

**Location: Dimwiddie 102
**

**Time: 3:30**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Hung Nguyen - Tulane University
**

**Abstract:
**

**Location: Gibson Hall
**

**Time: 3:00**

**Kristi Vandusen and Padi Fuster - Tulane University
**

**Abstract:
**

**Secret Meeting of the L5 Society
**

**Location: Stanley Thomas 316
**

**Time: 4:15**

**Speaker - Institution
**

**Abstract:
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**Location:
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**Time:**

**Speaker - Institution
**

**Abstract:
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**Location:
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**Time:**

**Mahir Bilen Can - Tulane University
**

**Abstract:
**

**Location: Gibson Hall 400A
**

**Time: 12:45**

**Rebecca Borchering - University of Florida
**

**Abstract:
**

In this talk, we compare popular continuum approximations for the invasion probability to its exact solution. In particular, methods known as "Diffusion (or Stochastic Differential Equation) Approximation" and "Exponential Approximation" are derived. We find analytical expressions for these approximations in the large population limit and then use numerical methods to evaluate the performance of the approximation methods for finite populations. Interestingly we find that the diffusion approximation fails to obtain the correct large population limit, but can perform well for small populations that experience near critical dynamics. The exponential approximation obtains the right large population limit in the supercritical regime, but fails to capture nonmontonic characteristics of the invasion probability for small to intermediate sized populations.

**Location: Gibson 126
**

**Time: 3:00**

**Lin Li - Tulane University
**

**Abstract:
**

From linear regression, I will introduce the penalty method such as ridge method and lasso method. However, in some cases, the variates have strong correlation with each other, then we can use the group lasso. After that, I will talk about SLOPE(sorted L-One Penalty Estimation), which is method similar to the lasso method and consider the false discovery rate as the criteria.

**Location: Stanley Thomas 316
**

**Time: 4:15**

**Tulane AWM/AMS Student Chapter present:**

**Speaker - Institution
**

**Abstract:**

**Time: 2:00**

**Dr. Arthur Sherman - National Institutes of Health
**

**Abstract:
**

**Location: Stanley Thomas 316
**

**Time: 3:00**

**Speaker - Institution
**

**Abstract:
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**Location:
**

**Time:**

**Prof. Ronghua Pan - Georgia Tech (host Kun Zhao)
**

**Abstract:
**

As one of the oldest nonlinear PDE systems, the compressible Euler equations has been studied by many outstanding mathematicians. However, some basic questions, such as the global existence of classical solution v.s. finite time blowup, are still open even in one space dimension. In this lecture, we will report our recent progress in this direction, including a complete understanding on isentropic flows, and a refreshed understanding on general adiabatic flows. This lecture is based on joint works with H. Cai, G. Chen, S. Zhu, and Y. Zhu.

**Location: Dinwiddie 102
**

**Time: 3:30**

**Mahir Bilen Can - Tulane University
**

**Abstract:
**

In this talk we present our recent progress on the diagonal actions of a reductive groups on product varieties of the form X_1 x X_2, where X_1 is a symmetric space and X_2 is a partial flag variety. In particular, we classify all such actions.

**Location: Gibson Hall 400A
**

**Time:12:45**

**David Herzog - Institution
**

**Abstract:
**

**Location: Gibson Hall 126
**

**Time: 3:00**

**Fang Sun - Tulane University
**

**Abstract:
**

**Location: Stanley Thomas 316
**

**Time: 4:15**

**DR. DAGANG YANG - Tulaner - Institution
**

**Abstract:
**

This talk is a brief introduction to Riemannian geometry. Namely, I will explain what is a Riemannian manifold, why should one be interested in Riemannian geometry, the meaning of the sign of the sectional curvature, and some well-known open problems in Riemannian geometry.

**Location: Dimwiddie Hall 102
**

**Time: 2:00**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

Week of February 3 - January 30, 2017

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

Robin Pemantle

**Abstract:**

**Exact enumeration in probability and combinatorics often leads to rational generating functions. These, in turn, lead to limit shapes, often more exotic than the generic Gaussian shape arising from a Central Limit Theorem. This motivates the study of the asymptotics of the coefficients of a rational power series**

** F(Z) = P(Z) / Q(Z) = sum_R a_R Z^R
**

**where Z = (z_1, ... , z_d) and R = (r_1, ..., r_d) are d-tuples. Estimating a_R from P and Q is both a theoretical problem and a problem in effective computation. I will discuss what we know about how to read limit shape behavior from P and Q (mostly from Q). The examples in the pictures will all be explained.
**

**
**

**
**

**Location: Dinwiddie 102
**

**Al Vitter - Tulane University
**

**Abstract:
**

This will be a continuation of my first talk. I will state the Hodge Conjecture and then talk about some aspects that show its subtlety and importance. The Hodge Conjecture concerns smooth (non-singular) complex projective varieties. It relates the purely algebraic structure of the variety to its topological/complex-analytic structure via its cohomology groups. I will begin by discussing in a relatively untechnical way, some of the mathematics needed to state clearly the Hodge Conjecture.

**Location: Gibson 400A**

**Time: 1:00**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Slivi Beyarslan - Tulane University
**

**Abstract:
**

**Location: Stanley Thomas 316
**

**Time: 4:15**

**Dr. Lisa Fauci - Tulane University
**

**Abstract:
**

From fertilization to birth, successful mammalian reproduction relies on interactions of elastic structures with a fluid environment. Sperm flagella must move through cervical mucus to the uterus and into the oviduct, where fertilization occurs. In fact, some sperm may adhere to oviductal epithelia, and must change their pattern of oscillation to escape. In addition, coordinated beating of oviductal cilia also drives the flow. Sperm-egg penetration, transport of the fertilized ovum from the oviduct to its implantation in the uterus and, indeed, birth itself are rich examples of elasto-hydrodynamic coupling.

We will discuss successes and challenges in the mathematical and computational modeling of the biofluids of reproduction. In addition, we will present reduced models that evoke intriguing questions in fundamental fluid dynamics.

**Location: Dinwiddie 102
**

**Time: 2:00**

**Speaker - Institution
**

**Abstract:
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**Location:
**

**Time:**

**Speaker - Institution
**

**Abstract:
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**Location:
**

**Time:**

**Al Vitter - Tulane University
**

**Abstract:
**

This will be the first of probably 2 talks. The Hodge Conjecture concerns smooth (non-singular) complex projective varieties. It relates the purely algebraic structure of the variety to its topological/complex-analytic structure via its cohomology groups. I will begin by discussing in a relatively untechnical way, some of the mathematics needed to state clearly the Hodge Conjecture. Then I will concentrate on some aspects that bring out (hopefully) the subtlety and importance of the conjecture.

**Location: Gibson Hall 400A
**

**Time: 4:00**

**Speaker - Institution
**

**Abstract:
**

**Location:
**

**Time:**

**Victor H. Moll - Tulane University
**

**Abstract:**

**
**

**Location: Stanley Thomas 316
**

**Time: 4:30**

**Speaker - Institution
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**Abstract:
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**Location:
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**Time:**

**Speaker - Institution
**

**Abstract:
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**Location:
**

**Time:**

Location: Lavin Bernick Center for University Life (building 29) - Kendall Cram Room

Location: Lavin Bernick Center for University Life (building 29) - Kendall Cram Room

**Speaker - Institution
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**Abstract:
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**Location:
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**Time:**

**Speaker - Institution
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**Abstract:
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**Location:
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**Time:**

**Speaker - Institution
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**Abstract:
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**Location:
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**Time:**

Mathematics Department, 424 Gibson Hall, New Orleans, LA 70118 504-865-5727 math@math.tulane.edu