# Past Events

## Instability and non-uniqueness in the Navier-Stokes equations

**Tuesday, July 26, 2022, 9:30 a.m.** through **Tuesday, July 26, 2022, 10:30 a.m.**

Vincent 570

Dallas Albritton (Princeton University)

It is not yet known whether Navier-Stokes solutions develop singularities in finite time. If they do, then the solutions can be continued beyond the singularities as Leray-Hopf solutions. It is therefore a fundamental question, Are Leray-Hopf solutions unique? The goal of this course is to present very recent developments in our understanding of this question.

We will begin by quickly reviewing the Navier-Stokes basics: dimensional analysis, the energy balance, pressure, weak solutions, perturbation theory, and weak-strong uniqueness. To save time, we will not present the complete proofs.

Next, we will explain aspects of the Jia, Sverak, and Guillod program (Jia-Sverak, Inventiones 2014, JFA 2015; Guillod-Sverak, arXiv 2017) and, in particular, how instability in self-similarity variables can generate non-uniqueness. We will briefly discuss bifurcations, stable and unstable manifolds, and, time permitting, a short proof of the existence of large self-similar solutions.

Finally, we will present the recent work (A.-Brue-Colombo, Ann. Math. 2022) which rigorously established non-uniqueness of Leray-Hopf solutions with forcing. We will present the main idea but focus on the spectral perturbation arguments.

No prior knowledge of the Navier-Stokes equations is required, though it might be beneficial to preview background on weak and mild solutions in, for example, Chapters 4 and 11 in Robinson-Rodrigo-Sadowski or Chapters 3 and 5 in Tsai.

## Inviscid damping, enhanced dissipation, and dynamical stability for Euler and Navier Stokes equations

**Monday, July 25, 2022, 3 p.m.** through **Monday, July 25, 2022, 4 p.m.**

Vincent 570

Hao Jia (University of Minnesota, Twin Cities)

In this sequence of lectures, we will introduce the classical stability problem for incompressible Euler and Navier Stokes equations. We will focus on the specific setting of the perturbative regime near a spectrally stable monotonic shear flow, and explain various dynamical phenomena, such as inviscid damping for the Euler equation and enhanced dissipation for the Navier Stokes equations in the high Reynolds number regime. Recent advances and further open problems will also be discussed if time permits.

## 1d scattering theory and its application to nonlinear dispersive equations

**Monday, July 25, 2022, 1:30 p.m.** through **Monday, July 25, 2022, 2:30 p.m.**

Vincent 570

Gong Chen (Georgia Institute of Technology)

In these lectures, I will introduce the spectral theory and the scattering theory associated with the 1d Schr\”odinger operator. Then I will illustrate how these tools can be used to understand and compute the large-time behaviors of nonlinear dispersive equations.

## Singularity formation in incompressible fluids and related models

**Monday, July 25, 2022, 11 a.m.** through **Monday, July 25, 2022, Noon**

Vincent 570

Jiajie Chen (California Institute of Technology)

Whether the 3D incompressible Euler equations can develop a finite-time singularity from smooth initial data is an outstanding open problem. In these lectures, we will describe some recent progress on singularity formation in incompressible fluids and related models. We will begin with some properties of the 3D Euler equations useful for studying singularity formation and the dynamic rescaling formulation of the 3D Euler equations. Then we will discuss some ideas to overcome some difficulties in singularity formation and study finite time blowup based on the stability of an approximate blowup profile. We will compare this stability and another notion of stability of blowup. Lastly, we will discuss some ideas for constructing finite time blowup from smooth initial data, particularly in 1D models of the Euler equations, which can be helpful in studying the singularity formation of 3D Euler with smooth data.

## Instability and non-uniqueness in the Navier-Stokes equations

**Monday, July 25, 2022, 9:30 a.m.** through **Monday, July 25, 2022, 10:30 a.m.**

Vincent 570

Dallas Albritton (Princeton University)

It is not yet known whether Navier-Stokes solutions develop singularities in finite time. If they do, then the solutions can be continued beyond the singularities as Leray-Hopf solutions. It is therefore a fundamental question, Are Leray-Hopf solutions unique? The goal of this course is to present very recent developments in our understanding of this question.

We will begin by quickly reviewing the Navier-Stokes basics: dimensional analysis, the energy balance, pressure, weak solutions, perturbation theory, and weak-strong uniqueness. To save time, we will not present the complete proofs.

Next, we will explain aspects of the Jia, Sverak, and Guillod program (Jia-Sverak, Inventiones 2014, JFA 2015; Guillod-Sverak, arXiv 2017) and, in particular, how instability in self-similarity variables can generate non-uniqueness. We will briefly discuss bifurcations, stable and unstable manifolds, and, time permitting, a short proof of the existence of large self-similar solutions.

Finally, we will present the recent work (A.-Brue-Colombo, Ann. Math. 2022) which rigorously established non-uniqueness of Leray-Hopf solutions with forcing. We will present the main idea but focus on the spectral perturbation arguments.

No prior knowledge of the Navier-Stokes equations is required, though it might be beneficial to preview background on weak and mild solutions in, for example, Chapters 4 and 11 in Robinson-Rodrigo-Sadowski or Chapters 3 and 5 in Tsai.

## 2022 UMN Summer Workshop on Analysis of PDEs

**Monday, July 25, 2022, 9 a.m.** through **Friday, July 29, 2022, 11:30 a.m.**

University of Minnesota

**Advisory: **

Note that the workshop is intended for graduate students and advanced undergraduates.

**Organizers: **

- Hao Jia, University of Minnesota, Twin Cities

In this five-day workshop for both graduate students and advanced undergraduate students, there will be a number of lectures given by active and leading experts in several important areas of analysis of partial differential equations, especially those arising from mathematical analysis of fluid dynamics and nonlinear waves. Participants will learn about the physical background, rigorous mathematical formulation, analytic tools, and latest developments in important PDE phenomena including singularity formation, uniqueness and non-uniqueness of weak solutions, stability mechanisms, and soliton resolution. Participants will also have many opportunities to interact with the lecturers in informal settings.

We will provide financial support to facilitate students' participation. To apply, please submit the following documents through the Workshop Application link at the top of the page:

- A brief CV or resume. (A list of publications is not necessary.);
- A reference letter from your advisor or professor.

Supported by NSF CAREER 1945179

### Schedule

Subscribe to this event's calendar

#### Monday, July 25, 2022

9:00 am - 9:30 am | Registration and Coffee | Vincent 502 |

9:30 am - 10:30 am | Instability and non-uniqueness in the Navier-Stokes equations
Dallas Albritton (Princeton University) |
Vincent 570 |

10:30 am - 11:00 am | Break and Discussion | Vincent 502 |

11:00 am - 12:00 pm | Singularity formation in incompressible fluids and related models
Jiajie Chen (California Institute of Technology) |
Vincent 570 |

12:00 pm - 1:30 pm | Lunch | |

1:30 pm - 2:30 pm | 1d scattering theory and its application to nonlinear dispersive equations
Gong Chen (Georgia Institute of Technology) |
Vincent 570 |

2:30 pm - 3:00 pm | Break | Vincent 502 |

3:00 pm - 4:00 pm | Inviscid damping, enhanced dissipation, and dynamical stability for Euler and Navier Stokes equations
Hao Jia (University of Minnesota, Twin Cities) |
Vincent 570 |

4:00 pm - 4:30 pm | Break and Discussion | Vincent 502 |

#### Tuesday, July 26, 2022

9:00 am - 9:30 pm | Coffee | Vincent 502 |

9:30 am - 10:30 am | Instability and non-uniqueness in the Navier-Stokes equations
Dallas Albritton (Princeton University) |
Vincent 570 |

10:30 am - 11:00 am | Break and Discussion | Vincent 502 |

11:00 am - 12:00 pm | Singularity formation in incompressible fluids and related models
Jiajie Chen (California Institute of Technology) |
Vincent 570 |

12:00 pm - 1:30 pm | Lunch | |

1:30 pm - 2:30 pm | 1d scattering theory and its application to nonlinear dispersive equations
Gong Chen (Georgia Institute of Technology) |
Vincent 570 |

2:30 pm - 3:00 pm | Break and Discussion | Vincent 502 |

3:00 pm - 4:00 pm | Inviscid damping, enhanced dissipation, and dynamical stability for Euler and Navier Stokes equations
Hao Jia (University of Minnesota, Twin Cities) |
Vincent 570 |

4:00 pm - 5:00 pm | Outdoor Group Activity |

#### Wednesday, July 27, 2022

9:00 am - 9:30 am | Coffee | Vincent 502 |

9:30 am - 10:30 am | Instability and non-uniqueness in the Navier-Stokes equations
Dallas Albritton (Princeton University) |
Vincent 570 |

10:30 am - 11:00 am | Break and Discussion | Vincent 502 |

11:00 am - 12:00 pm | Singularity formation in incompressible fluids and related models
Jiajie Chen (California Institute of Technology) |
Vincent 570 |

12:00 pm - 1:30 pm | Lunch | |

1:30 pm - 2:30 pm | 1d scattering theory and its application to nonlinear dispersive equations
Gong Chen (Georgia Institute of Technology) |
Vincent 570 |

2:30 pm - 3:00 pm | Break and Discussion | Vincent 502 |

3:00 pm - 4:00 pm | Inviscid damping, enhanced dissipation, and dynamical stability for Euler and Navier Stokes equations
Hao Jia (University of Minnesota, Twin Cities) |
Vincent 570 |

4:00 pm - 4:30 pm | Break and Discussion | Vincent 502 |

#### Thursday, July 28, 2022

9:00 am - 9:30 am | Coffee | Vincent 502 |

9:30 am - 10:30 am | Instability and non-uniqueness in the Navier-Stokes equations
Dallas Albritton (Princeton University) |
Vincent 570 |

10:30 am - 10:45 am | Group Photo | |

10:45 am - 11:00 am | Break and Discussion | Vincent 502 |

11:00 am - 12:00 pm | On the long-term regularity of water waves
Alexandru Ionescu (Princeton University) |
Vincent 570 |

12:00 pm - 1:30 pm | Lunch | |

1:30 pm - 2:30 pm | On the long-term regularity of water waves
Alexandru Ionescu (Princeton University) |
Vincent 570 |

2:30 pm - 3:00 pm | Break and Discussion | Vincent 502 |

3:00 pm - 4:00 pm | Singularity formation in incompressible fluids and related models
Jiajie Chen (California Institute of Technology) |
Vincent 570 |

4:00 pm - 4:30 pm | Break and Discussion | Vincent 502 |

4:30 pm - 5:00 pm | Panel Discussion | Vincent 570 |

#### Friday, July 29, 2022

8:30 am - 9:00 am | Coffee | Vincent 502 |

9:00 am - 10:00 am | Inviscid damping, enhanced dissipation, and dynamical stability for Euler and Navier Stokes equations
Hao Jia (University of Minnesota, Twin Cities) |
Vincent 570 |

10:00 am - 10:30 am | Break and Discussion | Vincent 502 |

10:30 am - 11:30 am | On the long-term regularity of water waves
Alexandru Ionescu (Princeton University) |
Vincent 570 |

### Participants

Name | Department | Affiliation |
---|---|---|

Dallas Albritton | Institute for Advanced Studies | Princeton University |

Adam Black | Department of Mathematics | Yale University |

Gong Chen | Department of Mathematics | Georgia Institute of Technology |

Jiajie Chen | Department of Applied and Computational Mathematics | California Institute of Technology |

Adriaan de Clercq | School of Mathematics | University of Minnesota, Twin Cities |

Kevin Dembski | Department of Mathematics | Duke University |

Samir Donmazov | Department of Mathematics | University of Kentucky |

Ziyang Gao | Mathematics | University of Minnesota, Twin Cities |

Jialun He | Department of Mathematics | State University of New York - Stonybrook |

Yupei Huang | Department of Mathematics | Duke University |

Alexandru Ionescu | Department of Mathematics | Princeton University |

Hao Jia | School of Mathematics | University of Minnesota, Twin Cities |

Aldis Kurmis | Department of Mathematics | University of Minnesota, Twin Cities |

Noah Lee | Department of Applied and Computational Mathematics | Princeton University |

Kexin Li | Department of Mathematics | University of Michigan |

Zhengjun Liang | Department of Mathematics | University of Michigan |

Jiaqi Liu | Department of mathematics | University of Southern California |

Tal Malinovitch | Department of Mathematics | Yale University |

Frederick Rajasekaran | Department of Mathematics | University of California, San Diego |

Xuanlin Shu | Department of Mathematics | Rutgers, State University of New Jersey |

Yixuan Wang | Department of Applied and Computational Mathematics | California Institute of Technology |

Kin Yau James Wong | Department of Mathematics | University of California, San Diego |

Yantao Wu | Department of Mathematics | Johns Hopkins University |

## Collaborative Workshop for Women in Mathematical Biology: Mathematical Approaches to Support Women’s Health

**Monday, June 20, 2022, 8:30 a.m.** through **Friday, June 24, 2022, 11:30 a.m.**

UnitedHealth Group-Minnetonka

**Advisory: **The deadline for application is March 18, 2022.

### Organizers

- Ashlee Ford Versypt — University at Buffalo (SUNY)
- Rebecca Segal — Virginia Commonwealth University
- Blerta Shtylla — Pfizer
- Suzanne Sindi — University of California, Merced

This five-day workshop focuses on collaborative research, in small groups of women, each group working on an open problem in a particular area of mathematical biology. Each group will include women at different career stages, from early career mathematicians to leaders in the field, to bolster leadership among senior mathematical biologists and data scientists, and to provide mentoring for early career mathematicians. Complementing the research time there will be activities engaging all participants, including career panels, discussions and building community.

Women researchers from underrepresented groups, working at universities with a teaching focus and small colleges, and those isolated geographically from potential collaborators, are especially encouraged to apply.

### Schedule

#### Monday, June 20, 2022

- 8:30–9:30am — Workshop Check-in (UnitedHealth Group-Minnetonka)
- 9:30am–12:00pm — Intro and Project Overviews
- 12–12:30pm — Quick Group Meeting
- 12:30–1:30 pm — Lunch (on site)
- 1:30–5pm — Group Research
- 5–7pm — Group Research

#### Tuesday, June 21, 2022

- 9am–12pm — Research
- 12–1pm — Lunch
- 1–2:30pm — Career Panel
- 2:30–5:30pm — Research

#### Wednesday, June 22, 2022

- 9am–12pm — Research
- 12pm–1pm — Lunch
- 1–2pm — Pair and Share
- 2–5:30pm — Research

#### Thursday, June 23, 2022

- 9am–12pm — Research
- 12–1pm — Lunch
- 1–5:30pm — Research

#### Friday, June 24, 2022

- 8:30–11:30am — Project Presentations / Wrap-up

### Participants

Name | Department | Affiliation |
---|---|---|

Jennifer Aduamah | Department of Mathematical Sciences | Rochester Institute of Technology |

Mukti Chowkwale | Department of Biomedical Engineering | University of Virginia |

Morgan Craig | Department of Applied Mathematics and Statistics | University of Montreal |

Angelica Davenport | Department of Mathematics | Florida State University |

Lisette de Pillis | Department of Mathematics | Harvey Mudd College |

Laura Ellwein Fix | Department of Mathematics and Applied Mathematics | Virginia Commonwealth University |

Ashlee Ford Versypt | Department of Chemical and Biological Engineering | University at Buffalo (SUNY) |

Katharine Gurski | Department of Mathematics | Howard University |

Alejandra Donaji Herrera Reyes | School of Mathematical Sciences | University of Nottingham |

Adrianne Jenner | School of Mathematics and Statistics | Queensland University of Technology |

Rachel Jennings | UHG Research & Development | UnitedHealth Group |

Yeona Kang | Department of Mathematics | Howard University |

Narges Kelly | Department of Physics | Brandeis University |

Amy Kent | Mathematical Institute | University of Oxford |

Ruby Kim | Department of Mathematics | Duke University |

Yena Kim | Department of Mathematics | Hawaii Pacific University |

Karin Leiderman | Department of Applied Mathematics and Statistics | Colorado School of Mines |

Kathryn Link | Department of Mathematics | University of California, Davis |

Samantha Linn | Department of Mathematics | The University of Utah |

Sharon Lubkin | Department of Mathematics | North Carolina State University |

Rayanne Luke | Department of Applied Mathematics and Statistics | Johns Hopkins University |

Ruiyan Luo | Population Health Sciences | Georgia State University |

Yanping Ma | Department of Mathematics | Loyola Marymount University |

Anna Nelson | Department of Mathematics | Duke University |

Jordana O'Brien | Department of Applied Mathematics | Rochester Institute of Technology |

Janet Oladejo | Pure and Applied Mathematics | Ladoke Akintola University of Technology |

Lucy Oremland | Department of Mathematics and Statistics | Skidmore College |

Jenna Ott | Department of Chemical and Biological Engineering | Princeton University |

Susan Rogowski | Department of Mathematics | Florida State University |

Rebecca Segal | Department of Mathematics | Virginia Commonwealth University |

Blerta Shtylla | Department of Early Clinical Development | Pfizer |

Robyn Shuttleworth | Department of Biology | University of Saskatchewan |

Suzanne Sindi | School of Natural Sciences | University of California, Merced |

Alexandra Smirnova | Department of Mathematics and Statistics | Georgia State University |

Melissa Stadt | Department of Applied Mathematics | University of Waterloo |

Melissa Stoner | Department of Mathematical Sciences | Salisbury State University |

Deborah Sundal | UHG Research & Development | UnitedHealth Group |

Diana White | Department of Mathematics | Clarkson University |

Lingyun Xiong | Department of Quantitative and Computational Biology | University of Southern California |

Sarah Youssef | UHG Research & Development | UnitedHealth Group |

Wenjing Zhang | Department of Mathematics and Statistics | Texas Tech University |

Ying Zhang | Department of Mathematics | Brandeis University |

Lihong Zhao | Department of Applied Mathematics | University of California, Merced |

Heather Zinn Brooks | Department of Mathematics | Harvey Mudd College |

### Projects and teams

#### Project 1: HIV, Pre-exposure prophylaxis, and drug resistance

- Katharine Gurski, Howard University
- Yeona Kang, Howard University

In December 2021, the FDA approved an injectable pre-exposure prophylaxis (PrEP) for use in at-risk adults and adolescents to reduce the risk of sexually acquired HIV. The cabotegravir extended-release injectable suspension is given first as two initiation injections administered one month apart, and then every two months thereafter. In this project, we aim to study how dynamics of drug-sensitive and drug-resistant HIV strains within hosts affect the prevalence of drug-resistant strains in the population when injectable pre-exposure prophylaxis enters the picture. This project will use methods from dynamical systems, statistics as it relates to sensitivity analysis, data, and parameter estimation and numerical simulation.

#### Project 2: Modeling the stability and effectiveness of dosing regimens of oral hormonal contraceptives

**Mentor**Lisette de Pillis, Harvey Mudd College- Heather Zinn Brooks, Harvey Mudd College

Oral contraceptives are a leading form of birth control in the United States, but consistent daily use and unwanted side effects can pose challenges for some users. Existing mathematical models of the effects of hormonal contraception on the menstrual cycle do not incorporate the dynamics of the on/off dosing regimens or the metabolism of the exogenous hormones, although methods from differential equations and dynamical systems are well-positioned to investigate these questions. We aim to explore the stability of the contraceptive state achieved by oral hormonal contraceptives using a mechanistic mathematical model of the menstrual cycle. Such a model could provide insight into when a contraceptive state is lost due to inconsistency or changes in hormonal birth control use, which may further inform the advisement of care providers and the choices of birth control users.

#### Project 3: Effects of exogenous-hormone induced perturbations on blood clotting

**Mentor**Karin Leiderman, Colorado School of Mines- Anna Nelson, Duke University

Exogenous hormones are used by hundreds of millions of people worldwide for contraceptives and hormonal replacement therapy (HRT). However, estrogen in combined oral contraceptives (OC) and HRT have been shown to significantly increase the risk of both arterial and venous thrombosis.The objectives for this project are to use a mechanistic mathematical model of flow-mediated coagulation to investigate the effects of exogenous-hormone induced perturbations that have been observed on blood clotting. We will use the model to simulate specified hormone induced perturbation profiles, i.e., percent changes in plasma levels of proteins and blood platelets caused by estrogen and progesterone, in varying doses, separately and together. The first objective will be to verify the observations from the literature showing increased clotting for specified profiles and doses. It is also well known that plasma levels of clotting factors vary among individuals. Variation that is considered normal and still healthy is a range between 50 and 150% of the mean value of the healthy population. Our second objective will be to identify individuals that may be more susceptible to thrombosis due to certain hormones and doses. We will accomplish this by performing global sensitivity analysis on model output metrics where variance is due to uncertainty in the input levels of clotting factors, platelets, and hormones.

#### Project 4: Development of effective therapeutic schedules in breast and gynecological cancers

- Morgan Craig, University of Montreal
- Adrianne Jenner, Queensland University of Technology

After lung cancer, breast cancer continues to be projected as the second most commonly diagnosed cancer in Canada. Leveraging data cancer growth, pharmacokinetic and pharmacodynamic models of various cancer therapies, and models of therapeutic resistance, this project aims to identify responders/non-responders to treatments and establish effective therapeutic schedules in breast and gynecological cancers. For this, we will develop mathematical and pharmacokinetic/pharmacodynamic models, integrated with patient data, to construct and implement in silico clinical trials. Familiarity with MATLAB, Python, and/or R is recommended. Other data fitting software including Monolix may be introduced, but prior knowledge is not necessary.

#### Project 5: Modeling neonatal respiratory distress

- Laura Ellwein Fix, Virginia Commonwealth University
- Sharon Lubkin, North Carolina State University

Respiratory distress in the newborn, a condition characterized by difficulty breathing, occurs in about 7% of newborns. This team’s project will address a question related to modeling of respiratory mechanics in the neonatal population. We previously developed an ordinary differential equations (ODE) model describing dynamic breathing volumes and pressures in aggregate compartments depicting the airways, lungs, chest wall, and intrapleural space, in an ideal spontaneously breathing preterm infant. Current areas of inquiry include application to ventilated infants and parameter identification using clinical data from a neonatal intensive care unit or an animal model. Alternatively, a specific unsolved problem could arise that requires the incorporation of a different dynamic model type such as spatially dependent or stochastic, or connects the organ level respiratory system with different physiology. The team’s co-leaders have interests in physiology, biotransport, tissues, cardiovascular and respiratory systems, and the use of noninvasive data in modeling. Our expertise centers on physiological mechanistic modeling, spatiotemporal systems and dynamics, parameter identification, numerics, and model development starting from simple to complex. Ideal team members would have interest and knowledge in some of these areas and embrace the opportunity to learn in other areas.

#### Project 6: On stable estimation of disease parameters and forecasting in epidemiology

- Ruiyan Luo, Georgia State University
- Alexandra Smirnova, Georgia State University

Real-time reconstruction of disease parameters for an emerging outbreak helps to provide crucial information for the design of public health policies and control measures. The goal of our team project is to investigate and compare parameter estimation algorithms that do not require an explicit deterministic or stochastic trajectory of system evolution, and where the state variable(s) and the unknown disease parameters are reconstructed in a predictor-corrector manner in order to mitigate the excessive computational cost of a quasi-Newton step. We plan to look at uncertainty quantification and implications of parameter estimation on forecasting of future incidence cases. Theoretical study will be combined with numerical experiments using synthetic and real data for COVID-19 pandemic.

## Math-to-Industry Boot Camp VII

**Monday, June 20, 2022, 8 a.m.** through **Wednesday, June 29, 2022, 5 p.m.**

Online

**Advisory: **Application deadline is March 21, 2022

Summer Math Boot Camp Vll poster

**Organizers:**

- Thomas Hoft, University of St. Thomas
- Daniel Spirn, University of Minnesota, Twin Cities

The Math-to-Industry Boot Camp is an intense six-week session designed to provide graduate students with training and experience that is valuable for employment outside of academia. The program is targeted at Ph.D. students in pure and applied mathematics. The boot camp consists of courses in the basics of programming, data analysis, and mathematical modeling. Students work in teams on projects and are provided with training in resume and interview preparation as well as teamwork.

There are two group projects during the session: a small-scale project designed to introduce the concept of solving open-ended problems and working in teams, and a "capstone project" that is posed by industrial scientists. Recent industrial sponsors included Gargill, Securian Financial and CH Robinson.

Weekly seminars by speakers from many industry sectors provide the students with opportunities to learn about a variety of possible future careers.

### Eligibility

Applicants must be current graduate students in a Ph.D. program at a U.S. institution during the period of the boot camp.

### Logistics

The program will take place online. Students will receive a $2,000 stipend.

### Applications

To apply, please supply the following materials through the link at the top of the page:

- Statement of reason for participation, career goals, and relevant experience
- Unofficial transcript, evidence of good standing, and have full-time status
- Letter of support from advisor, director of graduate studies, or department chair

Selection criteria will be based on background and statement of interest, as well as geographic and institutional diversity. Women and minorities are especially encouraged to apply. Selected participants will be contacted in April.

### Projects and teams

#### CH Robinson: Team 1 — Dynamic pricing in logistics

**Mentor**Brady Thompson, CH Robinson**Mentor**Veronika Koubova, CH Robinson**Mentor**Matthew Smith, CH Robinson**Mentor**Orion Wynblatt, CH Robinson**Mentor**Daniel Prentice, CH Robinson- Ibrahem Aljabea, Louisiana State University
- Abhinav Chand, Kansas State University
- Mengting Chao, University of Maryland
- Zhaobidan (Amy) Feng, Texas A & M University
- Vanny Khon, Boston University
- Christian McRoberts, Iowa State University

Pricing in logistics is a very fast paced environment. Pricing managers need to be aware of the constant changes in the market, and be able to adapt quickly. Depending on the business needs, whether that be to increase profit or increase volume, we need to be able to quickly explore the data, develop a model, and test to determine if the strategy is meeting the business goals. Our team of data scientists work in Less-Than-Truckload pricing, a fast growing market segment driven by recent trends in the supply chain. Given a business goal, we use historical data to build a pricing strategy that we believe will achieve the goal, and then run controlled experiments to determine the success of our strategy.

A boot camp student working on our project would become familiarized with dynamic pricing, as well as research surrounding multi-choice pricing dynamics. They will develop the python skills needed to implement machine learning models that use historical and streaming data, including reinforcement learning. Lastly, it is expected that they would be able to manage an online controlled experiment to test the quality of their pricing strategy.

#### ITM TwentyFirst: Team 2 — Identifying Longevity Risk with Machine Learning

**Mentor**Jonathan Hill, ITM TwentyFirst LLC**Mentor**Tianze Li, ITM TwentyFirst LLC- Shan Chen, University of Minnesota, Twin Cities
- Haridas Kumar Das, Oklahoma State University
- Kimberlyn Eversman, University of Tennessee
- Dumindu Sandakith Kasiwatte Kankanamge, Vanderbilt University
- Mark Roach, Michigan State University
- Matthew Wynne, University of Washington

Traditional approaches to predicting life outcomes are robust and interpretable but come with limitations. They are limited in the number of interactions between medical conditions (“comorbidities”) that can be considered, unable to handle missing values, and have a fixed base table shape. We developed a machine learning model (the Longevity Risk Model) to address these limitations. Its target is to identify insureds where our traditional model (“RevH”) is likely too long (low longevity risk) or too short (high longevity risk). Our goal is to expand the ideas behind the Longevity Risk Model and find creative ways to improve its predictions. These improvements might include, but are not limited to, identifying COVID deaths in our dataset and adding COVID as a feature to the model, using quantile objective functions to make prediction intervals, altering the structure of the stacked models, and predicting the conditional probability of outliving life expectancy.

We will use Python 3, along with a unique world-class dataset on senior life outcomes provided by ITM TwentyFirst, a Minneapolis-based life settlements servicing company.

#### US Bank: Team 3 — Forecasting Prepayments in High Interest Rate Environment

**Mentor**Chistopher Jones, US Bank- Caroline Bang, Iowa State University
- Katheryn Beck, University of Kansas
- Zanbing Dai, University of Minnesota, Twin Cities
- Leonardo Digiosia, Rice University
- Arpan Pal, Texas A & M University
- Bo Zhu, University of Minnesota, Twin Cities

U.S. agency 1 residential mortgage-backed securities (MBS) are the largest and most liquid securitized asset class in the world. Banks, insurance companies, and money managers invest in MBS because they provide an attractive yield relative to U.S. Treasury securities with comparable credit risk. However, unlike most fixed income securities, which have specified contractual coupon and principal payments, the timing and amount of MBS cash flows is uncertain. This is because MBS are pools of individual mortgages on which the borrower has the right to prepay the loan at any given time during the life of the loan. Prepayment risk, which impacts the yield and interest rate risk of an MBS comes from five sources:

Rate/term refinance which occur when borrowers lower interest payments or shorten the term of the current mortgage.

Cash-out refinance which involve extracting equity from a home.

Involuntary buyouts, which in the case of agency MBS result in an early return of principal. However, the timing is contingent on the GSEs or GNMA loan servicers.

Curtailments, which are partial prepayment or full payoff before maturity.

Turnover, which is caused by geographic migration and home upgrades. Turnover creates a baseline level of prepayments that are highly seasonal.

The COVID-19 crisis and response by the Federal Reserve resulted in a low-rate environment that elevated both levels of refinance and buyout activity. Since the initiation of quantitative tightening, sustained inflation, and rising interest rates, refinance activity has slowed considerably. At present, a major question affecting the risk profile of MBS is to what extent prepayment activity will decrease. With diminishing refinance incentives, the major sources of prepayment are now turnover, curtailment, and buyouts. As a baseline level of prepayment activity, understanding turnover is important to evaluating the risks of mortgage-backed securities. The goal of this project is to use loan-level mortgage data and macroeconomic data to quantify turnover prepayment speed.

## Roots of Unity Workshop

**Sunday, June 12, 2022, 8 a.m.** through **Thursday, June 16, 2022, 5 p.m.**

University of Minnesota, Twin Cities

**Advisory: **

- Please see below for detailed application instructions.
- The deadline for application is February 28, 2022.

### Organizers

- Christine Berkesch — University of Minnesota, Twin Cities
- Michelle Manes — University of Hawaii
- Priyam Patel — The University of Utah
- Candice Price — Smith College
- Adriana Salerno — Bates College
- Bianca Viray — University of Washington

### Apply

To apply, please submit the following documents:

#### 1. Personal Statement**.**

Please write a brief (max 5,000 character) statement describing your interest in attending the Roots of Unity workshop. We are interested in understanding how your identities have impacted your mathematical journey, as well as your areas of interest and approximate timeline for choosing an advisor. To the extent that you feel comfortable sharing, please describe your journey, possibly including: your experiences collaborating with, supporting, and being supported by your peers, particularly those from groups marginalized in mathematics, and any obstacles that you have faced. On two separate additional pages in this document (that is not part of the max character count), please provide: (i) a list of the graduate courses you have taken in topics related to the workshop, and (ii) your ranking of topic preferences for the working groups (arithmetic geometry, combinatorics, commutative algebra, geometry, topology).

#### 2. Resume or CV

#### 3. One letter of reference

One letter of reference from someone who can speak to your potential in your graduate program. Your letter-writer will be emailed instructions on how to upload their letter to MathPrograms. Please email your letter-writer the following sentences:

I am asking you to provide a brief letter of reference to support my application to the Roots of Unity workshop. This week-long workshop is designed to support women, particularly women of color, who have completed 1–3 years of graduate school and are considering research in algebra, combinatorics, geometry, topology, or number theory. The program would appreciate your candid opinion of me as a student, including in what capacity you have worked with me, my potential for success in my graduate program in the mathematical sciences, how the Roots of Unity workshop might benefit me, and how I will benefit the Roots of Unity workshop. For more information about the workshop, please see the Roots of Unity website.

### Workshop description

This week-long workshop is designed to support women, particularly women of color, who are in years 1–3 of graduate school and are considering research in algebra, combinatorics, geometry, topology, or number theory.

In a forest, underground mycorrhizal networks connect different tree species through their root systems, allowing for transfer of nutrients (van der Heijden, 2016). These networks also allow trees to communicate about dangers like pests and disease, and they are believed to enhance plant fitness and forest stability. For graduate students, too, a strong network can be critical for success, and such networks are even more important for students from groups that have been historically marginalized. We have designed the Roots of Unity workshop to assist in cultivating strong relationships among the participants, a network — seeded at the workshop and continuing throughout their careers — that will allow students to strengthen and nurture each other.

The transition to independent learning and research is a crucial and often jarring point in every graduate student's career. This transition is even more difficult for students from marginalized groups, who often have smaller support systems and may face an actively unsupportive environment at their institution. The goal of this workshop is to support, mentor, and guide students at this crucial stage in their career.

During the workshop, mentors will guide the student participants through the (often very daunting!) experience of trying to read a paper without being an expert in the area. The participants will be broken into small working groups, each focused on a recent paper in their area of interest. Each group will be assisted throughout the week by mentors, both early career mathematicians (late stage graduate students or postdocs) and faculty members.

The professional development component of the Roots of Unity Workshop will focus on practical tools for navigating a research career, while building community and increasing access to professionals or near-peers. These will include in-person panels and activities during the workshop and follow-up (virtual) activities throughout the year to continue nurturing the community and connections.

The program is tailored to support women of color, and our strategies reflect this priority. However, if you are a graduate student in your first three years of study and believe that this workshop will benefit you, please apply. We especially encourage applications from students who are women, nonbinary, and/or gender fluid.

Applications received by February 28, 2022, will receive full consideration. Application decisions will be sent out no later than March 31, 2022.

### Workshop groups

**Commutative Algebra**

Mentors: Christine Berkesch, Haydee Lindo, Patricia Klein

**Combinatorics **

Mentors: Pamela Harris, Mariel Supina, Isabelle Shankar

**Low Dimensional Topology and Geometry **

Mentors: Candice Price, Emille Davie, Sherilyn Tamagawa

**Geometry **

Mentors: Autumn Kent, Marissa Loving, Michelle Chu

**Arithmetic Geometry **

Mentors: Adriana Salerno, Lori Watson, Allechar Serrano Lopez

## Developing Online Learning Experiments Using Doenet (2022)

**Monday, May 23, 2022, 8 a.m.** through **Thursday, May 26, 2022, 5 p.m.**

University of Minnesota, Twin Cities

## Organizers

- Jim Fowler — The Ohio State University
- Kris Hollingsworth — University of Minnesota, Twin Cities
- Duane Nykamp — University of Minnesota, Twin Cities
- Matt Thomas — Cornell University

In this four-day workshop, participants will learn how to create and implement online learning experiments using the Distributed Open Education Network (Doenet, doenet.org). Doenet is designed to help faculty critically evaluate how different content choices influence student learning in their classrooms. Doenet enables instructors to quickly test hypotheses regarding the relative effectiveness of alternative approaches by providing tools to assign different variations of an activity and analyze the resulting data.

Following brief introductions and demos of features of the Doenet platform, participants will work in small groups to develop learning experiments that can be used in the college classroom, assisted by the developers of Doenet. The expectation is that participants will leave the workshop with a learning experiment that they can use in their classroom the following year.

The workshop will run from 9 AM on Monday, May 23 though noon on Thursday, May 26. All organized activities will occur between 9 AM and 4 PM each day.

The workshop is open to faculty at all levels teaching STEM courses; instructors of mathematics courses are particularly encouraged to apply.

To apply, please submit the following documents through the Program Application link at the top of the page:

- A personal statement briefly (200 words or less) stating what you hope to contribute to the discussion on learning experiments and what you hope to gain from this workshop. Include courses you teach for which you'd like to develop learning experiments. Priority will be given to those able to run learning experiments in their courses in the following year.
- A brief CV or resume. (A list of publications is not necessary.)

This workshop is fully funded by the National Science Foundation. All accepted participants who request funding for travel and/or local expenses will receive support. There is no registration fee.

Participants who perform learning experiments on Doenet during the following academic year will be eligible to receive a small stipend to support their work.

Supported by NSF grant DUE 1915363.