Join us for these events hosted by the Department of Mathematics, including colloquia, seminars, graduate student defenses and outreach, or of interest to Mathematicians hosted by other groups on campus.

# Upcoming Events

### Welcome Back Tea!

Welcome back to a new academic year! Join us for a special edition of tea time. We'll have special tasty snacks -- did someone say doughnuts? -- and we'll renew the caption contest. Come, relax, and unwind with your friends and colleagues in the math department. Read more.

### Three Vignettes in Applied Topology

**Speaker:** Chad Giusti

A fundamental tool in applied topology is persistent homology, which measures how the topological structure of a parameterized space evolves with the parameter. This measurement is usually given in the form of a persistence diagram (PD), which encodes the isomorphism type of the resulting algebraic structure. By vectorizing PDs for parameterized complexes built out of observed data, standard statistical methods allow us to use these estimates to infer organization and structure of observed systems. However, simply comparing PDs is often insufficient to solve interesting problems. In this talk, we will survey three of our recent projects in applied topology that go beyond computation of static PDs: 1. Time-varying systems naturally produce paths of PDs. While vectorization schemes for PDs can be naively extended to this setting, these extensions lack important theoretical properties. Leveraging Chen's classical iterated integral construction, we develop a robust feature set for… Read more.

### Sesquiharmonic Maass forms and class numbers of real quadratic fields

**Speaker:** Michael Allen

### Organizational Meeting

Join us at the for the first P&D seminar meeting! We will have brief introductions and we’ll discuss plans for the rest of the term. This is great opportunity to get to know the probability group. Read more.

### TBA

**Speaker:** Taranjot Kaur

In an ever-changing natural world, both plants and pollinators are continually confronted by perturbations. Responses to such perturbations can ripple from populations to communities through networks of interacting species. Additionally, the response to perturbations can unfold at various timescales ranging from short-term behavioral processes at the individual level to long-term population persistence. The goal of the work I will present in my talk is to evaluate how responses to perturbations propagate through timescales in plant-pollinator communities. Specifically, we use mathematical tools of non-linear averaging and stochastic processes to investigate how disturbances at shorter timescale of nectar regeneration scale to long-term outcomes of abundances of plants and pollinators. Furthermore, we study the impact of temporal correlation in stochasticity, network structure, and adaptive foraging dynamics on this scale transition framework. Read more.

### Fokas Diagonalization

**Speaker:** Dave Smith

We describe a new form of diagonalization for linear two point constant coefficient differential operators with arbitrary linear boundary conditions. Although the diagonalization is in a weaker sense than that usually employed to solve initial boundary value problems (IBVP), we show that it is sufficient to solve IBVP whose spatial parts are described by such operators. We argue that the method described may be viewed as a reimplementation of the Fokas transform method for linear evolution equations on the finite interval. The results are extended to multipoint and interface operators, including operators defined on networks of finite intervals, in which the coefficients of the differential operator may vary between subintervals, and arbitrary interface and boundary conditions may be imposed; differential operators with piecewise constant coefficients are thus included. BIO: Dave Smith is an Applied Mathematician working at Yale-NUS College, Singapore since 2016. He completed his… Read more.

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**Speaker:** Patrick Phelps

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**Speaker:** Jerry Shurman

Note atypical date and time. Read more.

### The Knave's Cosmological Theorem

**Speaker:** Tamsyn Morrill

Abstract: The Look-Say sequence is a classic example of recursion. Its terms are verbalized descriptions of their predecessors --- initialized at 1 --- 11, 21, 1211, and so on. Conway demonstrated that the asymptotic growth rate of this sequence is the unique real root of a degree 71 monic polynomial. The general idea is to recast the problem in linear algebra through use of his Cosmological Theorem. Today I present a variation of this problem. A knave (of Smullyan's famed door-keeper puzzle) now controls the recursion. After working through some small examples, we will remake the Cosmological Theorem in the knave's image. Read more.

### Traces of Hecke Operators via Hypergeometric Character Sums

**Speaker:** Fang-Ting Tu

### Global Sensitivity Analysis of Plasma Instabilities via Active Subspaces

**Speaker:** Stephen Pankavich

The dynamics of laboratory and space plasmas are often driven by potentially uncertain values of physical parameters. For this reason, the utilization of computational methods to quantify such uncertainty represents an important tool to understand how certain physical phenomena depend upon fluctuations in the values of these parameters. In this direction, I'll discuss the construction and implementation of new computational methods, called active subspace methods, to quantify the induced uncertainty within the (linear) stability/instability rates generated by perturbations in a collisionless plasma near spatially homogeneous equilibria. BIO: Steve Pankavich is a Professor in the Department of Applied Mathematics and Statistics at the Colorado School of Mines, where he has served as a faculty member for 11 years. He earned a PhD in Mathematical Sciences from Carnegie Mellon University and was a Zorn Postdoctoral Fellow at Indiana University. Prior to joining Mines, he also held a… Read more.

### TBA

**Speaker:** Kazuo Yamazaki

### Direct methods for inverse problems in the shear wave elastography field

**Speaker:** Olalekan Babanyi

Shear wave elastography is a technique used to noninvasively estimate the mechanical properties of tissue from propagating mechanical waves. These mechanical properties can be used to noninvasively diagnose and help with the treatment of various diseases like cancer, and liver fibrosis. The mechanical properties can also be used to understand various biological processes like wound healing, and cell division. To compute the mechanical properties, one needs to solve an inverse problem governed by differential equation models. I will present several direct variational formulations that can be used to efficiently solve the inverse problem. I will discuss some of the mathematical properties of these variational formulations, and compare their performance on simulated data. BIO: Olalekan Babaniyi is currently an assistant professor in the School of Mathematics and Statistics at Rochester Institute of Technology (RIT). Prior to joining RIT, he was a post-doctoral scholar at the… Read more.

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**Speaker:** Bella Tobin

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**Speaker:** Manami Roy

### Regularization Methods for Inverse Problems in Imaging

**Speaker:** Malena Espanol

Discrete linear and nonlinear inverse problems arise from many different imaging systems, exhibiting inherent ill-posedness wherein solution sensitivity to data perturbations prevails. This sensitivity is exacerbated by errors arising from imaging system components (e.g., cameras, sensors, etc.), necessitating the development of robust regularization methods to attain meaningful solutions. Our presentation commences with the exposition of distinct imaging systems, and their mathematical formalism, and subsequently introduces regularization techniques tailored for linear inverse problems. Then, we delve into the variable projection method, a powerful tool to address separable nonlinear least squares problems. BIO: Malena Español is an Assistant Professor in the School of Mathematical and Statistical Sciences at Arizona State University. She has a Bachelor's in Applied Mathematics from the University of Buenos Aires and a Master's and PhD in Mathematics from Tufts University; she was… Read more.

### Development of the Arctic Coastal Erosion Model with a Demonstration at Drew Point, AK

**Speaker:** Jennifer Frederick

Erosion is accelerating along many stretches of the coastal Arctic, putting critical infrastructure at risk and threatening local communities. These permafrost-laden coastlines are increasing vulnerable to erosion due to declining sea ice and increasing duration of open water, more frequent storms during ice-free periods, and warming permafrost soils. However, predicting shoreline erosion rate remains extremely challenging because of the highly non-linear behavior of the coupled and changing environmental system. Although the Arctic comprises one-third of the global coastline and has some of the fastest eroding coasts, current tools for quantifying permafrost erosion are unable to explain the episodic, storm-driven erosion events. In this talk I will present the details of the development and calibration efforts for the Arctic Coastal Erosion (ACE) Model at Sandia National Laboratories. The ACE Model is a multi-physics numerical tool that couples oceanographic and atmospheric… Read more.

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**Speaker:** Maja Taskovic

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**Speaker:** Eugnhyun Lee

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**Speaker:** Eunghyun Lee

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**Speaker:** Linda Cummings