**Week of April 20 - April 24**

Graduate Student Colloquium

**Topic:** *Graphs and Geometry*

**Victor Bankston | Tulane University**

**Abstract:**

We will introduce the Collin de Verdiere Invariant and discuss its relation to graph embedding problems.

**Meeting Id:** 913-3840-9369

**Meeting URL:** https://tulane.zoom.us/j/91338409369

**Date:** April 14' 2020

**Time:** 4.30 pm

**Week of April 13 - April 17**

Graduate Student Colloquium

**Topic:** *p-adic valuations of polynomials*

**Vaishavi Sharma | Tulane University**

**Meeting Id:** 913-3840-9369

**Meeting URL:** https://tulane.zoom.us/j/91338409369

**Time:** 4.30 pm

**Week of April 3 - March 30**

Graduate Student Colloquium

**Topic:** *Bruhat posets of Hermitian-type symmetric spaces*

**Aram Bingham | Tulane University**

**Abstract:**

Compact irreducible Hermitian symmetric spaces come in four infinite families. In each case, their complexifications yield an associated affine bundle over a Grassmannian π: G/L→G/P. I'll discuss the Bruhat poset of containments of Borel orbit closures in the total space G/L.

**Time: 4.30 pm **

**Sankhaneel Bisui is inviting you to a scheduled Zoom meeting.**

**Topic: Graduate-Zoom-talk-Aram
Time: Mar 31, 2020 04:30 PM Central Time (US and Canada)**

**Join Zoom Meetinghttps://tulane.zoom.us/j/604266778**

**Meeting ID: 604 266 778**

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**Week of March 27 - March 23**

Graduate Student Colloquium

**Topic:** *What is local cohomology?*

**Thai Nguyen | Tulane University**

**Abstract:**

Local cohomology was introduced by Alexander Grothendieck in the 1960s as a tool to study sheaves and their cohomology in algebraic geometry. Since then, commutative algebraists have used it widely and found various applications. In this talk, I will try to explain this notion from an algebraic point of view by discussing an application of it.

**Meeting Id: **899-652-418

**Meeting URL: **https://tulane.zoom.us/j/899652418

**Time: **4:30

**Week of March 13 - March 2**

Canceled

~~Geometry and Topology~~

**Topic:** *Metric reconstruction and Borsuk-Ulam theorems*

**Henry Adams - Colorado State University**

**Abstract:**

~~The Vietoris-Rips complex is a standard construction to attempt to recover M from X up to homotopy type. Given a sample of points X in a metric space M and a scale r > 0, the Vietoris-Rips complex is a standard construction to attempt to recover M from X up to homotopy type. A deficiency is that the Vietoris-Rips simplicial complex may not be metrizable if X is infinite, and therefore need not recover metric information about M. We remedy this shortcoming by defining the Vietoris-Rips metric thickening via the theory of optimal transport. With this machinery, we can say more about the homotopy type of Vietoris-Rips thickenings of n-spheres. As an application, we give generalizations of the Borsuk-Ulam theorem for maps from the n-sphere into higher-dimensional codomains R^k with k >= n.~~

**Location: **Gibson Hall 308**Time: **12:30

Canceled

Algebra & Combinatorics

**Topic:** *Some multiplicity one theorems for wreath products*

**Yiyang She - Tulane University**

**Abstract:**

Let G be a group and let H be a subgroup.

If all irreducible representations of G restrict to multiplicity free H representations, then (G,H) is said to be a strong Gelfand pair.

In this talk we will present our recent results on the strong Gelfand pairs of finite wreath products.

This is a joint work with Mahir Bilen Can and Liron Speyer.

**Location: **Gibson Hall 127**Time: **3:00

Canceled

~~Graduate Student Colloquium~~

**Topic:** *The Borel Submonoid of a Symplectic Monoid*

**Hayden Houser | Tulane University**

**Abstract:**

~~In this talk, we consider the combinatorial properties of the complex symplectic monoid $MSp_n$. We provide a concrete description of the Bruhat-Chevalley-Renner order on $MSp_n$ by showing that this partial order is completely determined by the Bruhat-Chevalley-Renner order on the algebraic monoid of $n \times n$ matrices $M_n$. We then develop a relationship between the Borel submonoid of $MSp_n$ and a new kind of type B set partitions.~~

**Location: **Stanley Thomas 316**Time: **4:30

Canceled

**Week of March 8 - March 9**

Colloquium

**Topic:** *Group actions and finite free complexes over polynomial rings*

**Srikanth B Iyengar - University of Utah (Host: Tai Ha)**

**Abstract:**

This talk will be about various results (some of recent vintage) and conjectures concerning finite free complexes over polynomial rings. Many of these concern numerical invariants associated with such a complex; notably, the length of the complex, and the ranks of the free modules that appear in it. This thread of research can be traced back to Hilbert's Syzygy Theorem (1890) that states that each finitely generated module over a polynomial ring over a field has a finite free resolution. The modern developments in this subject started with the work of Auslander, Buchsbaum, and Serre in the 1950s, and have since then been a centerpiece in commutative algebra. Another impetus for the subject has come from results and conjectures of Adem, Browder, Carlsson, Halperin, and Swan, among others, on obstructions to groups acting freely on spaces.

**Location: **Gibson Hall 126A**Time: **3:30

Geometry and Topology

**Topic:** *Symplectic Geometry of Anosov Flows in Dimension 3 and bi-Contact Topology*

**Surena Hozoori - Georgia Tech**

**Abstract:**

Anosov flows, introduced by Dmitri Anosov in the 1960s, define an important and well-studied class of hyperbolic dynamics and are known to have subtle relation to the topology of the underlying manifold, in particular in dimension 3. Exploring natural geometric quantities associated with an Anosov flow, we will give a purely contact and symplectic geometric characterization of such flows in dimension 3 and set a framework for using well known and effective methods in contact topology to understand questions in Anosov dynamics.

**Location: **Gibson Hall 308**Time: 12:30**

Algebra & Combinatorics

**Topic:** *The Borel Submonoid of a Symplectic Monoid*

**Tewodros Amdeberhan | Tulane University**

**Abstract:**

The symplectic monoid MSp_n of this talk is the semisimple monoid that is obtained from the defining representation of the symplectic group Sp_n. The Zariski closure of a Borel subgroup of MSp_n is called a Borel submonoid of MSp_n.

In this talk, we will discuss some geometric and combinatorial properties of the symplectic Borel submonoids. On the combinatorial side, we will show that there is a new type BC set partition combinatorics associated with these objects.

On the geometric side, we will show that such Borel submonoids are rationally smooth varieties. Consequently, our new set partitions can be used for computing the intersection cohomology Betti numbers of the symplectic Borel submonoids. This is a joint work with Hayden Houser and Corey Wolfe.

**Location: **Gibson Hall 127**Time: **3:00

Graduate Student Colloquium

**Topic:** *Points and Containments*

**Sankhaneel Bisui | Tulane University**

**Abstract:**

In this talk, I will describe projective space and different algebraic sets in the space and the corresponding algebraic objects. Many commutative algebraists, Algebraic Geometers are interested in containment problems of the ideals corresponding to the points. One of the motives to study the containment is to get a better lower bound on the least degree of the hypersurfaces that pass through the points. I will also describe some of these problems and some results about them.

**Location: **Stanley Thomas 316**Time: **4:30

**Week of February 28 - February 24**

~~Applied and Computational Cancelled~~

**Topic:** *Spectral properties of quasicrystals*

**Jake Fillman | Texas State**

**Abstract:**

~~Discovered by D. Shechtman in the early 1980s, quasicrystals are materials whose molecular structure is characterized by aperiodicity (the absence of translation symmetries) and long-range order. The study of these objects involves a beautiful synthesis of many areas of mathematics, including topology, dynamical systems, harmonic analysis, and spectral theory. We will introduce background and discuss operator-theoretic models of quasicrystals. Along the way, we will highlight interesting features of these models, recent progress, and open problems.~~

**Location: **Gibson Hall 310**Time: **3:00

~~Applied and Computational Cancelled~~

Algebra & Combinatorics

**Topic:** *Classical Mechanics, Symplectic Geometry, Combinatorics*

**Tewodros Amdeberhan | Tulane University**

**Abstract:**

In this semi-expository talk, we give a brief on classical mechanics in the Hamiltonian setting, describe it in the symplectic framework and draw out some interesting combinatorics. The discussion will be accessible to all.

**Location: **Gibson Hall 127**Time: **3:00

**Week of February 21 - February 17**

Applied and Computational Mathematics

**Topic:** *A perfect numerical scheme for large-scale geophysical flows?*

**Qingshan Chen | Clemson**

**Abstract:**

A new scheme, based on the vorticity and divergence variables, is developed using the the Hamiltonian approach. The scheme operates on unstructured meshes over a globe or a bounded domain, conserves both energy and enstrophy, and possesses the optimal dispersive wave relations, which is crucial for the maintenance of the geostrophic balance within the flow. The main ideas behind the derivation will be reviewed, and results from a suite of test cases will be presented to demonstrate the superior advantages as well as the limitations of the new scheme.

**Location: **Gibson Hall 310**Time: **3:00

Graduate Student Colloquium

**Topic:** *Competitive Programming*

**Akshay Mehra | Tulane University**

**Abstract:**

Many companies gauge the programming skills of a candidate based on their ability to solve complex problems and their ability to code the solution in some programming language. Moreover, coding rounds are a part of the interview process for companies such as Google, Facebook, Apple, Amazon, etc, even when you apply for their research positions. Hence, in order to be prepared for these interviews, it’s extremely important to be competent in at least one programming language and have experience in coming up with algorithms to solve challenging problems with their complexity analysis. In this talk, I intend to give a short introduction about how to approach these interview problems and will interactively solve 2 such problems. This will demonstrate the power of algorithms and will be helpful to you when you are searching for a job or an internship in the industry.

**Location: **Stanley Thomas 316**Time: **4:30

**Week of February 10 - February 14**

Colloquium

**Topic:** *Symbolic powers*

**Eloísa Grifo - California, Riverside (Host: Tai Ha)**

**Abstract:**

The main goal of this talk it to introduce symbolic powers and discuss what the main open problems in this area are. Symbolic powers arise naturally from the theory of primary decomposition, an extension of the fundamental theorem of arithmetic. These are algebraic objects that also contain geometric information. Hilbert's Nullstellensatz gives a dictionary between algebra and geometry: solution sets to polynomial equations over the complex numbers (varieties) translate to (radical) ideals in polynomial rings. A classical theorem of Zariski and Nagata gives a deeper layer to this correspondence: polynomial functions that vanish up to a certain order along a variety correspond to symbolic powers.

**Location: **Gibson Hall 126A**Time: 3:30**

AWM Coffee discussion

**Topic:** *Coffee Discussion*

**Eloísa Grifo - **University of California, Riverside

**Abstract:**

The AWM chapter is organizing coffee discussion with this week's colloquium speaker, Eloisa Grifo from University of California, Riverside

This is an informal meeting to have coffee and good conversation with our colloquim speaker. Come say hi!

**Location: **Stanley Thomas 316**Time: **11:00

Algebra & Combinatorics

**Topic:** *Symbolic powers and the (stable) containment problem*

**Eloísa Grifo | UC Riverside**

**Abstract:**

The n-th power of an ideal is easy to compute, though difficult to describe geometrically. In contrast, symbolic powers of ideals, which arise naturally from the theory of primary decomposition, are difficult to compute but have a natural geometric description.

In trying to compare symbolic and ordinary powers, Harbourne conjectured that a famous containment by Ein--Lazersfeld--Smith, Hochster--Huneke, and Ma--Schwede could be improved. Harbourne's Conjecture is a statement depending on n that has been disproved for particular values of n. However, recent evidence points towards a stable version of Harbourne's conjecture, where we substitute all n by all n large enough. Some of that evidence is joint work with Craig Huneke and Vivek Mukundan.

**Location: **Gibson Hall 127**Time: **3:00

Colloquium

**Topic:** *A probabilistic framework for models of dependent network data, with statistical guarantees*

**Jonathan Stewart | Rice University**

**Abstract:**

The statistical analysis of network data has attracted considerable attention since the turn of the twenty-first century, fueled by the rise of the internet and social networks and applications in public health (e.g., the spread of infectious diseases through contact networks), national security (e.g., networks of terrorists and cyberterrorists), economics (e.g., networks of financial transactions), and more. While substantial progress has been made on exchangeable random graph models and random graph models with latent structure (e.g., stochastic block models and latent space models), these models make explicit or implicit independence or weak dependence assumptions that may not be satisfied by real-world networks, because network data are dependent data. The question of how to construct models of random graph with dependent edges without sacrificing computational scalability and statistical guarantees is an important question that has received scant attention.

In this talk, I present recent advancements in models, methods, and theory for modeling networks with dependent edges. On the modeling side, I introduce a probabilistic framework for specifying edge dependence that allows dependence to propagate throughout the population graph, with applications to brokerage in social networks. On the statistical side, I obtain the first consistency results in settings where dependence propagates throughout the population graph and the number of parameters increases with the number of population members. Key to my approach lies in establishing a direct link between the convergence rate of maximum likelihood estimators for exponential families and the scaling of the Fisher information matrix. Last, but not least, on the computational side I demonstrate how the conditional independence structure of models can be exploited for local computing on subgraphs, facilitating development of parallel computing algorithms for multi-core computers or computing clusters.

**Location: **Hebert 212**Time: 4:00**

Graduate Student Colloquium

**Topic:** *Stokes flow due to regularized forces between parallel planes*

**Dana Ferranti | Tulane University**

**Abstract:**

We present a method to compute Stokes flows due to regularized Stokeslets which are periodic in the x and y directions, and confined between two walls in the z-direction. The primary goal of the study is to simulate microorganism motility in confined geometries. Preliminary results from this ongoing work will be presented.

**Location: **Stanley Thomas 316**Time: **5:00

**Week of February 7 - February 3**

Applied and Computational

**Topic:** *Classical Mechanics, Simplectic Geometry, Combinatorics*

**Teddy Amdeberhan | Tulane**

**Postponed to March 27, at 3:00 pm, Gibson Hall 310**

Colloquium

**Topic:** *How Can Mathematics Save the Honeybees?*

**Yun Kang | Arizona State University (Host: James Hyman)**

**Abstract:**

The honeybee is crucial in maintaining biodiversity by pollinating 85% of the world’s plant species. This bee is the most economically valuable pollinator of agricultural crops worldwide. Recently the Varroa mite has infected honeybee hives and caused sharp declines in honeybee populations, resulting in a global crisis. I will demonstrate how we develop tractable mathematical models to clarify the principal mechanisms responsible for colony growth dynamics and survival in a dynamic environment. The mathematical analysis of these models can help us understand the crucial feedback mechanisms linking disease, parasitism, nutrition, and foraging behavior. We consider both nonlinear nonautonomous and delayed differential equations. The models are integrated with data to create a metapopulation framework for exploring the contributing factors to the mysterious and dramatic loss of honeybees. We use numerical simulations to identify new strategies for controlling Varroa, reducing colony losses for beekeepers, and maximizing the benefits for land managers.

**Location: **Gibson Hall 126A**Time: 3:30**

AWM

**Topic:** *AWM coffee discussion*

**Yun Kang | Arizona State University **

**Abstract:**

Coffee Discussion

**Location: **Stanley Thomas 404**Time: **11:00

Colloquium

**Topic:** *Reproducible Bootstrap Aggregating*

**Meimei Liu | Duke University**

**Abstract:**

Heterogeneity between training and testing data degrades reproducibility of a well-trained predictive algorithm. In modern applications, how to deploy a trained algorithm in a different domain is becoming an urgent question raised by many domain scientists. In this paper, we propose a reproducible bootstrap aggregating (Rbagging) method coupled with a new algorithm, the iterative nearest neighbor sampler (INNs), effectively drawing bootstrap samples from training data to mimic the distribution of the test data. Rbagging is a general ensemble framework that can be applied to most classifiers. We further propose Rbagging+ to effectively detect anomalous samples in the testing data. Our theoretical results show that the resamples based on Rbagging have the same distribution as the testing data. Moreover, under suitable assumptions, we further provide a general bound to control the test excess risk of the ensemble classifiers. The proposed method is compared with several other popular domain adaptation methods via extensive simulation studies and real applications including medical diagnosis and imaging classifications.

**Location: **Hebert Hall 213**Time: **2:00

Graduate Student Colloquium

**Topic:** *Enumeration of restricted Dyck paths*

**Diego Rubiano Villamizar | Tulane University**

**Abstract:**

In this talk, we will discuss the combinatorics of a family of Dyck paths by imposing conditions on the vector of altitudes of the valleys. This is joint work with Rigoberto Florez, Jose L. Ramirez, and Fabio Velandia.

**Location: **Stanley Thomas 316**Time: **4:30

**Week of January 31 - January 27**

Colloquium

**Topic:** *Tropical Algebraic Geometry*

**Kalina Mincheva - Yale University**

**Abstract:**

Tropical geometry provides a new set of purely combinatorial tools to approach classical problems in algebraic geometry. The fundamental objects in tropical geometry are tropical varieties -- combinatorial ``shadows" associated to more traditional geometric objects, algebraic varieties. Until recently, the theory has focused on the geometric aspects of tropical varieties as opposed to the underlying algebra, largely due the lack of tropical analogues to commutative algebra tools. Consequently, there has recently been a lot of effort dedicated to developing such tools using different frameworks -- notably prime congruences, tropical ideals, and tropical schemes. These approaches allow for the exploration of tropical spaces as inherently tropical objects. In this talk, we present a notion of prime congruences and discuss the resulting analogues to classical theorems, such as a Nullstellensatz and aspects of dimension theory. We also demonstrate connections to algebraic geometry via the theory of tropical schemes and ideals.

**Location: **Gibson Hall 126A**Time: 3:30**

Algebra & Combinatorics

**Topic:** *Total nonnegativity and induced sign characters of the Hecke algebra*

**Mark Skandera - Lehigh University**

**Abstract:**

Gantmacher's study of totally nonnegative (TNN) matrices in the 1930's eventually found applications in many areas of mathematics. Descending from his work are problems concerning TNN polynomials, those polynomial functions of n^2 variables which take nonnegative values on TNN matrices. Closely related to TNN polynomials are functions in the Hecke algebra trace space whose evaluations at certain Hecke algebra elements yield polynomials in N[q]. In all cases, it would be desirable to combinatorially interpret the resulting nonnegative numbers. In 2017, Kaliszewski, Lambright, and the presenter found the first cancellation-free combinatorial formula for the evaluation of all elements of a basis of V at all elements of a basis of the Hecke algebra. We will discuss a recent improvement upon this result which also advances our understanding of TNN polynomials. This is joint work with Adam Clearwater.

**Location: **Gibson Hall 127**Time: **3:00

Colloquium

**Topic:** *Numerical methods for ocean models and venous valve simulations*

**Sara Calandrini - Florida State University**

**Abstract:**

**Location: **Stanley Thomas 316**Time: **3:00

Graduate Student Colloquium

**Topic:** *A PDE model for chemotaxis with logistic growth*

**Jiao Xu & Padi Fuster - Tulane University**

**Abstract:**

In this talk, we will derive a PDE model for chemotaxis (the movement of an organism in response to a chemical stimulus) with logistic growth. We will discuss the general derivation of the model and on what phenomena this can be applied to. We will also briefly talk about our results on the existence of solutions for this system of PDE.

**Location: **Stanley Thomas 316**Time: **4:30

Colloquium

**Topic:** *Quantum and symplectic invariants in low-dimensional topology.*

**Nathan Dowlin - Columbia University**

**Abstract:**

Khovanov homology and knot Floer homology are two powerful knot invariants developed around two decades ago. These invariants have been applied to problems all over low-dimensional topology, from detecting exotic smooth structures on 4-manifolds to determining whether a given knot diagram is the unknot. Knot Floer homology is defined using symplectic techniques, while Khovanov homology has its roots in the representation theory of quantum groups. Despite these differences, they seem to have many structural similarities. A well-known conjecture of Rasmussen from 2005 states that for any knot K, there is a spectral sequence from the Khovanov homology of K to the knot Floer homology of K. Using a new family of invariants defined using both quantum and symplectic techniques, I will give a proof of this conjecture and describe some topological applications.

**Location: **Stanley Thomas 316**Time: **2:00

**Week of January 24 - January 20**

Colloquium

**Topic:** *Modeling and simulation of symmetry breaking in cells*

**Calina Copos - New York University**

**Abstract:**

In order to initiate movement, cells need to form a well-defined "front" and "rear" through the process of cellular polarization. Polarization is a crucial process involved in embryonic development and cell motility and it is not yet well understood. Mathematical models that have been developed to study the onset of polarization have explored either biochemical or mechanical pathways, yet few have proposed a combined mechano-chemical mechanism. However, experimental evidence suggests that most motile cells rely on both biochemical and mechanical components to break symmetry. We have identified one of the simplest quantitative frameworks for a possible mechanism for spontaneous symmetry breaking for initiation of cell movement. The framework relies on local, linear coupling between minimal biochemical stochastic and mechanical deterministic systems; this coupling between mechanics and biochemistry has been speculated biologically, yet through our model, we demonstrate it is a necessary and sufficient condition for a cell to achieve a polarized state.

**Location: **Stanley Thomas 316**Time: **3:00

Colloquium

**Topic:** *Hessenberg varieties and the Stanley--Stembridge conjecture*

**Martha Precup - Washington U in St Louis (Host: Mahir Can)**

**Abstract:**

Hessenberg varieties are subvarieties of the flag variety with important connections to representation theory, algebraic geometry, and combinatorics. In 2015, Brosnan and Chow proved the Shareshian-Wachs conjecture, linking the Stanley-Stembridge conjecture in combinatorics to the geometry of Hessenberg varieties through Tymoczko's permutation group action on the cohomology ring of regular semisimple Hessenberg varieties. This talk will give an overview of that story and present a new set of linear relations satisfied by the multiplicities of certain permutation representations in Tymoczko's representation. As an application of these results, we prove an inductive formula for the multiplicity coefficients corresponding to partitions with a maximal number of parts. This is joint work with M. Harada.

**Location: **Gibson Hall 126A**Time: 3:30**

AWM Coffee discussion

**Topic:** *Coffee Discussion*

**Martha Precup - Washington U in St Louis**

**Abstract:**

The AWM chapter is organizing coffee discussion with this week's colloquium speaker, Martha Precup from Washington University in St.Louis.

This is an informal meeting to have coffee and good conversation with our colloquim speaker. Come say hi! There will be coffee and cookies! Don't forget your reusable mugs.

**Location: **Stanley Thomas 404**Time: 11:00**

Algebra & Combinatorics

**Topic:** *Gorenstein polytopes*

**Takayuki Hibi - Osaka University**

**Abstract:**

A Gorenstein polytope is a lattice polytope one of whose dilated polytopes is a reflexive polytope. In my talk, after reviewing Gorenstein polytopes from a viewpoint of enumeration of lattice points, several conjectures arising from Gorenstein polytopes will be reported. No special knowledge will be required to understand my talk.

**Location: **Gibson Hall 127**Time: **3:00

Graduate Student Colloquium

**Topic:** *Shape Comparison and Gromov-Hausdorff Distance*

**Sushovan Majhi | Tulane University**

**Abstract:**

The Gromov-Hausdorff distance between any two metric spaces was first introduced by M. Gromov in the context of Riemannian manifolds. This distance measure has recently received increasing attention from researchers in the field of topological data analysis. In applications, shapes are modeled as abstract metric spaces, and the Gromov-Hausdorff distance has been shown to provide a robust and natural framework for shape comparison. In this talk, we will introduce the notion and address the difficulties in computing the distance between two Euclidean point-clouds. In the light of our recent findings, we will also describe an O(n log n)-time approximation algorithm for Gromov-Hausdorff distance on the real line with an approximation factor of (1+ 1/4).

**Location: **Stanley Thomas 316**Time: **4:30

Colloquium

**Topic:** *Math in the lab: mass transfer through fluid-structure interactions*

**Jinzi Mac Huang - University of California San Diego**

**Abstract:**

The advancement of mathematics is closely associated with new discoveries from physical experiments. On one hand, mathematical tools like numerical simulation can help explain observations from experiments. On the other hand, experimental discoveries of physical phenomena, such as Brownian motion, can inspire the development of new mathematical approaches. In this talk, we focus on the interplay between applied math and experiments involving fluid-structure interactions -- a fascinating topic with both physical relevance and mathematical complexity. One such problem, inspired by geophysical fluid dynamics, is the experimental and numerical study of the dissolution of solid bodies in a fluid flow. The results of this study allow us to sketch mathematical answers to some long standing questions like the formation of stone forests in China and Madagascar, and, how many licks it takes to get to the center of a lollipop. We will also talk about experimental math problems at the micro-scale, focusing on the mass transport process of diffusio-phoresis, where colloidal particles are advected by a concentration gradient of salt solution. Exploiting this phenomenon, we see that colloids are able to navigate a micro-maze that has a salt concentration gradient across the exit and entry points. We further demonstrate that their ability to solve the maze is closely associated with the properties of a harmonic function – the salt concentration.

**Location: **Stanley Thomas 316**Time: **3:30

**Week of January 17 - January 13**

Algebra and Combinatorics

**Topic:** *Decomposable Specht modules*

**Liron Speyer - Okinawa Institute of Science and Technology**

**Abstract:**

I will give a brief survey of the study of decomposable Specht modules for the symmetric group and its Hecke algebra, which includes results of Murphy, Dodge and Fayers, and myself, before reporting on recent work with Louise Sutton, in which we have studied decomposable Specht modules for the Hecke algebra of type $B$ indexed by `bihooks’. I will present our conjectured classification of decomposable Specht modules indexed by bihooks, which we proved `one half of’, and some ongoing work in explicitly determining the structure of those decomposable Specht modules.

**Location: **Gibson Hall 127**Time: **3:00

Colloquium

**Topic:** *From Zariski-Nagata to local fundamental groups*

**Jack Jeffries - Mathematics Research Center, Mexico**

**Abstract:**

Hilbert's Nullstellensatz gives a dictionary between algebra and geometry; e.g., solution sets to polynomial equations over the complex numbers (varieties) translate to (radical) ideals in polynomial rings. A classical theorem of Zariski-Nagata gives a deeper layer to this correspondence: polynomial functions that vanish to certain order along a variety correspond to a natural algebraic notion called symbolic powers.

In this talk, we will explain this theorem, and then pursue a couple of variations on this theme. First, we will consider how the failure of this theorem over ambient spaces with bends and corners allows us to study the geometry of such spaces; in particular, we will give bounds on size of local fundamental groups. Second, we will consider what happens when we replace the complex numbers by the integers; we will show that "arithmetic differential geometry" (in the sense of Buium) allows us to obtain a Zariski-Nagata theorem in this setting. Only a passing familiarity with polynomials and complex numbers is assumed.

This is based on joint projects with Holger Brenner, Alessandro De Stefani, Eloísa Grifo, Luis Núñez-Betancourt, and Ilya Smirnov.

**Location: **Stanley Thomas 316**Time: **2:00

Research Seminar Name

**Topic:** *Title*

**Speaker - Institution**

**Abstract:**

TBA

**Location: **TBA**Time: **TBA