Monday, March 27, 2017 at 5:30 PM

Perkins 101

Math Club will be hosting a **peer advising course review** on **Monday, March 27 at 5:30pm in Perkins 101**.

Come learn about the best classes to take. We will focus on math classes, but if you have questions about other classes, we can try to answer those too.

No faculty will be present at this event, only students.

See you there!

]]>Tuesday, April 11, 2017, 7:00 - 8:30 PM

Waterman Memorial Lounge

The Department of Mathematics and Statistics will host a Statistics and Data Science career panel discussion on Tuesday, April 11 from 7:00 - 8:30 PM in Waterman Memorial Lounge.

Come learn about career opportunities in these fields. All are welcome, and we hope to see you there!

Eric Sandberg, National Life Group

Jeff Solomon, UTC Aerospace Systems

Brian Orleans, ICF International

Lucy Greenberg, Vermont Oxford Network

John Stanton-Geddes, Dealer.com

Polly Mangan, Dealer.com

Cody Rock, Vermont Department of Health

Lane Manning originally graduated from UVM in 2008 with a double-major Bachelor of Arts in physics and applied mathematics. He returned for a PhD in Materials Science, graduating last May. During his grad school days, Lane served as president of the Graduate Student Senate for several years and as a student representative on the Board of Trustees Educational Policy and Institutional Resources Committee. Now he's "Dr. Lane Manning" and is plunging into a career in the burgeoning photonics industry, employed by an England-based manufacturer.

But while Lane is the most recent member of his family to earn a UVM degree, he's by no means the first. In fact, Ardrey Manning counts no fewer than 11 members of her family who have attended UVM, dating all the way back to Lane's great-great-great-grandfather, former Vermont Governor Roswell Farnham.

Lane Manning went to work last year for AVR Optics, which makes optical filters, laser diodes, spatial light modulators and the like for research labs. Photonics is:

the science and technology of generating, controlling, and detecting photons, which are particles of light. [It] underpins technologies of daily life from smartphones to laptops to the Internet to medical instruments to lighting technology. ("What is Photonics")

As AVR ramps up North American operations, Lane will be calling on university and government labs, including NASA and a number of Nobel Prize winners.

If that sounds like the start of a promising career, Lane has a ways to go to match the luster of his gubernatorial ancestor. For starters, Gov. Farnham, a native of Bradford, breezed through his four-year degree program in just two years, graduating in 1849. After UVM, he taught school, practiced law, held many state offices, served with distinction as Lt. Col. of the 12th Vermont Volunteers (in what he called "the war for the suppression of the Rebellion"), and was elected to the state's top office in 1880 by a then-historic margin of 25,012 votes.

Republicans were, of course, a more liberal breed in those days. Looking back, in his 1882 farewell address, Lane's great-great-great-grandfather was proud to note that tax revenues grew by some 35 percent during his tenure and that the State Prison in Windsor now had "better lighted, better warmed and better ventilated buildings." Inmate education, he stressed, was the key to rehabilitation.

The governor was also pleased to report that things looked good for the University's State Agricultural College, thanks to the generous gifts of John P. Howard Esq., who among other things, "provided the means for erecting a statue of Lafayette in the park in front of the college buildings, the cornerstone of which the General laid in 1825."

It's a lot for Lane to live up to. Then again, old Roswell probably didn't even know the difference between a spatial light modulator and a … you know, the other kind of light modulator.

]]>University of Rochester

Friday, March 24, 2017

Kalkin 001

4:30 - 5:30 PM

**Abstract:**

The Kakeya "needle" problem, posed by S. Kakeya in 1918, is a classical question in analysis that asks how small a subset of the Euclidean plane can be, if it contains a unit line segment in every possible direction. This question was answered by A. Besicovitch in 1919, who gave the rather surprising answer that such sets can have area zero, but necessarily still had dimension 2. It remains open to this day, however, whether the minimal dimension of such a "Kakeya set" in n-dimensional Euclidean space must be n. In the late 1990s, T. Wolff proposed an algebraic version of the Besicovitch-Kakeya problem in the setting of a finite field, and a major advance in this area was made by Z. Dvir in 2008 using a stunning idea known as the "polynomial method". In this broad-audience talk, I will discuss the Kakeya problem in algebra and analysis along with some work of myself and others on bridging the gap between the algebraic and analytic versions of this problem.

ADA: Individuals requiring accommodations please contact Doreen Taylor at 802-656-3166

]]>Cornell University

Tuesday, February 21, 2017

Decision Theater, 107 Farrell Hall

4:15 - 5:15 PM

**Abstract:**

We usually think of algebra over rings of characteristic 0 and character p as being distinct. For example, if G is a finite group, the behavior of modules over its group ring with coefficient field k depends strongly on the characteristic of k. For example, if k is the complex numbers, indecomposable modules are irreducible and so all modules are projective, but this is not the case if k is a finite field of characteristic p dividing the order of G. Furthermore, the rings themselves are often endowed with natural "extra" structures that have no analogues in the other setting, such as Frobenius morphisms in characteristic p that do not exist in characteristic 0. So it may seem hopeless to try and find a unifying theory that fully explains the divergent behavior in both zero and nonzero characteristic. But surprisingly, some recent developments (with roots in some seemingly forgotten parts of mathematics) have been able to do precisely this! In particular, it has led to a robust theory of objects that are sort of in "intermediate" characteristic between 0 and p, or probably more accurately, in "positive characteristic p that is very close to zero." What do such objects look like geometrically? We will give some indications by explaining a simple combinatorial method for constructing geometric objects over mixed characteristic rings that yield these "tiny characteristic" objects in the limit and point towards some interesting questions raised by the existence of such a method.

ADA: Individuals requiring accommodations please contact Doreen Taylor at 802-656-3166

]]>A team of scientists have invented a new instrument for measuring just that: the caloric content of social media posts--like tweets.

"This can be a powerful public health tool," says Peter Dodds, a scientist at the University of Vermont, who co-led the invention of the new device--called a Lexicocalorimeter. "It's a bit like having a satellite image of how people in a state or city are eating and exercising."

A study of the new device was published February 10, in the journal PLOS ONE.

Of course, people don't actually eat tweets. Instead, the Lexicocalorimeter gathers tens of millions of geo-tagged Twitter posts from across the country and fishes out thousands of food words -- like "apples," "ice cream," and "green beans." At the same time, it finds thousands of activity-related terms -- like "watching TV," "skiing," and even "alligator hunting" and "pole dancing." These giant bags of words get scored--based on data about typical calorie content of foods and activity burn rates -- and then compiled into two measures: "caloric input" and "caloric output."

The ratio of these two measures begins to paint a picture that might be of interest not just to athletes or weight-watchers, but also to mayors, public health officials, epidemiologists, or others interested in "public policy and collective self-awareness," the team of scientists write in their new study.

The Lexicocalorimeter is open for visits by the public, and the current version gives a portrait of each of the contiguous US states. For example, the tweet flow into the device suggests that Vermont consumes more calories, per capita, than the overall average for the US. Why? Well, at the top of its list of words that push the Green Mountain State to the gourmand's side of the ledger is "bacon" -- tied for second in the US when states are ranked by bacon's contribution to caloric balance. "We love to tweet about bacon," says Chris Danforth, a UVM scientist and mathematician who co-led the new study.

But Vermont also expends more calories than average, the device indicates, thanks to relatively frequent appearances of the words "skiing," "running," "snowboarding," and, yes, "sledding." And why does the Lexicocalorimeter suggest that New Jersey expends fewer calories than the US average? Below-average on "running," while the top of its low-intensity activity list is "getting my nails done."

Overall, Colorado ranks first in the US for its caloric balance ("noodles" plus "running" seem to be a svelte pair), while Mississippi comes in last with relatively high representation of "cake" and "eating."

*A map of the Lexicocalorimeter’s “calories in” findings. Vermont: big on “bacon” and “skiing.” Michigan: “chocolate candy” and “laying down.” This instrument gathers tens of millions of Twitter posts and could become a powerful remote-sensing tool for public health officials. The results were published in the journal PLOS ONE. (Map: UVM/PLOS ONE)*

The new PLOS ONE study suggests that the Lexicocalorimeter could provide a new -- and real-time -- measure of the U.S. population's health. And the study shows that the device's remotely sensed results correlate very closely with other traditional measures of U.S. well-being, like obesity and diabetes rates. For the study, the team of scientists explored about 50 million geo-tagged tweets from 2011 and 2012 and report that "pizza" was the dominant contributor to the measure of "calories in" in nearly every state. The dominant contributor to calories out: "watching TV or movies."

The nine scientists -- including the new study's lead authors, former UVM graduate students Sharon Alajajian and Jake Williams, doctoral student Andy Reagan, and others at the University of Vermont's Computational Story Lab as well as researchers at the University of California Berkley, WIC in East Boston, MIT, University of Adelaide, and Drexel University -- are quick to point out that the ratio of calories in to calories out in the new study are "not meaningful as absolute numbers, but rather have power for comparisons."

The Lexicocalorimeter is part of a larger effort by the University of Vermont team to build a series of online instruments that can quantify health-related behaviors from social media. "Given the right tools, our mobile phones will very soon know more about us than we know about ourselves," says UVM's Chris Danforth. "While the Lexicocalorimeter is focused on eating and exercise, and the Hedonometer is measuring happiness, the methodology we're building is far more general, and will eventually contribute to a dashboard of public health measures to complement traditional sources of data."

The bigger goal: "enable real-time sensing at the population level, and help health care providers make data-driven recommendations for public policy," says Danforth.

Other measures of public health and behavior the team is considering adding to the dashboard? "Sleep is a huge health issue," says UVM's Peter Dodds. "We would like to make an Insomniameter. Then there could be a Hangoverometer."

]]>Residential-Workplace Neighborhood Effects on Body Mass Index

Professor of Biostatistics

Department of Biomedical Data Science

The Dartmouth Institute for Health Policy and Clinical Practice

Geisel School of Medicine at Dartmouth

4:15 PM

Waterman 427A

**Abstract:**

Hierarchical modeling is the preferred approach of modeling

neighborhood effects. Given residential and workplace location

indicators, a bivariate (residential-workplace) neighborhood random

effect whose correlation quantifies the extent that a neighborhood's

residential effect correlates with its workplace effect may be

specified. However, statistical model estimation software typically does

not allow correlations between the effects of different clustering

variables. In this talk, I develop a Bayesian model with a bivariate

random effect for neighborhood and an accompanying estimation procedure.

The model accounts for individuals who reside or work in multiple

neighborhoods across their observations, individual heterogeneity

(random intercepts, random slopes), and serial correlation between

observations on the same individual. We apply the models to linked

Framingham heart study – food establishment data to examine whether (i)

Proximity to fast-food establishments is associated with Body Mass Index

(BMI); (ii) Workplace neighborhood exposure associations are larger than

those for residential exposure; (iii) Residential neighborhood exposure

associations correlate with workplace neighborhood exposure. For

robustness, we evaluate these hypotheses under multiple specifications

of the prior distribution of the neighborhood random effect covariance

matrix. In addition, we show that allowing for time varying neighborhood

membership, individual heterogeneity, and serial correlation across time

yields more precise neighborhood level estimates.

A double-major in mathematics and statistics, with a minor in computer science, Strayer started putting data visualizations on his website when he was an undergrad. “Basically, what I do is make numbers tell a story through pictures,” he says. For example, in the summer after his junior year, he was working for a data visualization start-up company in California and there were a lot of forest fires. “It was fifteen miles each way to work,” he recalls. “ I didn't want to bike if the smoke was really bad. But there were no good tools online to see where wildfires were burning.” So he built one himself. “I went and found some data that NASA had opened up from their satellites that pinpoint temperature anomalies on the surface of the planet.” Strayer’s goal was simply to have a “map on my phone that I could check out and see: hey, should I bike today?” he says. But it was such a good tool that he soon got a call from the Red Cross. They wanted to use it to help with rescue efforts.

**Nick Strayer had a simple goal: make a wildfire map so he could avoid smoke on his bike commute. But it attracted the attention of the Red Cross and helped lead him to a story about wildfires that he published in the New York Times.**

During his senior year, Strayer worked with researchers at UVM’s Gund Institute for Ecological Economics to create a “narrative visualization” of the effects of different policies on global warming. His goal: to help a team of UVM scientists that was heading to the UN climate negotiations in Paris. Afterward, he got a message on Twitter from an editor at the *New York Times*, who “liked what I was doing,” Strayer says. Soon, he had a summer internship at the newspaper and was cranking out stories and images, including several for The* *Upshot, the *Times'* quantitative blog—and a 20-hour workday to build a block-by-block visualizaton of the terrorist attack in Nice, France.

One of Strayer’s stories drew wide national attention and echoed with his own story of going to college—having left a small farm town in Michigan to come to Vermont. “The Great Out-of-State Migration: Where Students Go,” presents a national map showing the number of first-year college students who left their home states to attend public college in another state. The flowing orange arrows make the story of this in-and-out migration seem, well, simple. But in truth it was so hard to uncover that it had never been told before. “I had to play with this data for a long time,” Strayer says in an understated Midwestern kind of way. He gathered lists of students from “thousands of public universities, each with its own systems, and all these weird codes,” he says. Soon after his story was published, Strayer received an email from a university researcher, an expert on school migration. “’Where did you get this data?’ he asked me. I’ve been searching for this for my whole career,” Strayer says.

Now Strayer is a PhD student in biostatistics at Vanderbilt—with his own independent funding from the NIH’s Big Data to Knowledge program—but he plans to continue contributing to the *New York Times*. “I’m going to go crazy on my next vacation to get some freelance pieces done for them,” he says, “I’ve got some stories in mind.”

And the power of stories is perhaps the most important lesson he learned as a student at UVM. Strayer’s discovery of what he calls “narrative insight” began on his very first day of class in the Honors College—when he had a paper due for professor Helga Schreckenberger’s freshman seminar, The Pursuit of Knowledge. “I’m a very quantitative, mathematically-minded person,” Strayer says, “and in high school I thought all this liberal arts stuff was stupid. I was naïve.” He got a poor grade on that paper—and began a close friendship with Schreckenberger, the chair of UVM’s German Department, who mentored him for four years. “She’s a wonderful person,” he says, “whose scholarly interests in exile narratives couldn’t be more different than mine,” he says, but “she helped me see that writing was more than simply putting words down on a page to get a good grade,” he said. “It’s a chance to connect.”

From her, as well as mathematicians James Bagrow and Richard Single, lake ecologist Jason Stockwell, and other professors, Strayer began to learn that the search for narrative allows knowledge, even the most quantitative, to illuminate “other people’s experience and to distill meaning,” he says. At its deepest, a story is a “form of empathy,” Nick Strayer says. “I’m looking for the deeper story in the data.”

]]>Williams College

Friday, December 2, 2016

4:00 - 5:00 PM

Kalkin 003

**Abstract:**

Let RS (resp., RA) denote the average number of runs scored (resp., allowed) in a baseball game by a team. It was numerically observed years ago that a good predictor of a team's won-loss percentage is

RS^{2} / (RS^{2} + RA^{2}), though no one knew WHY the formula worked. We review elementary concepts of probability and statistics, and discuss how one can build and solve a model for this problem. We'll discuss how to attack problems like this in general (what are the features of a good model, how to solve it, how does one do new research which people will care about, and so on). We mention some of the standard statistical tests, and sketch the proof of the most famous, the Central Limit Theorem. The only pre-requisite is simple calculus (no baseball knowledge is required, though Red Sox knowledge is always a plus).

**ADA: Individuals requiring accommodations please contact Doreen Taylor at 802-656-3166**

Dartmouth

4:30 - 5:30 PM

Kalkin 002

**Abstract:**

The Fast Fourier Transform (FFT) is a family of algorithms underlying a large range of important applications in digital signal processing and data analysis. In this talk we consider the FFT from the point of view of harmonic analysis for semisimple algebras and present some recent results related to FFTs for various families of finite groups and finite-dimensional algebras. This is joint work with David Maslen and Sarah Wolff.

ADA: Individuals requiring accommodations please contact Doreen Taylor at 802-656-3166

]]>December 3, 2016

The William Lowell Putnam Mathematical Competition is an annual contest for college students established in 1938. Substantial cash prizes are awarded to the top five teams and to the top five individuals. In 1997, the Elizabeth Lowell Putnam Prize was established to honor the top woman competitor.

The 2016 Putnam exam will take place on Saturday, December 3, 2016. As usual, there will be two three-hour sessions starting at 10:00 a.m. and 3:00 p.m., held in the Math Dept Conference Room, 16 Colchester Ave. While the competition for the prizes is very strong, all students should enjoy and benefit from the experience of taking part in the most prestigious mathematical contest in the country.

Registration forms listing participants are due by October 7 (so we have to mail ours by October 4). Here is some additional information about the competition:

- The Department provides lunch for all participants on the day of the competition at a nearby restaurant.
- Sample problems from recent competitions are available from members of the committee.
- Only “regularly enrolled undergraduate students” may participate (students have a lifetime maximum of 4 times). Registering at the outset guarantees that we will have a slot for the student; but he/she may decide, even at the last minute, not to come (it’s no problem!). Some students stay only for the morning session and lunch (which is OK too). Unregistered “walk-ins” may also participate (unregistered students may take the place of registered students who don’t show up too – so there are usually ample “walk-in” slots).
- Students must arrive by 9:50 a.m. to participate in the Competition. A student may not take the afternoon portion without first having attended the morning session.
- Each session consists of six (challenging) problems, most of which can be answered with calculus and a little linear algebra (and a healthy dose of ingenuity).
*Advanced course work is not required.* - The committee will hold one or two
*optional*training sessions to review some potentially useful problem-solving skills. Solutions to past exams will be available for interested students. These sessions are low-key, fun and informal, where students take the lead in discussing practice problems (that we will circulate beforehand). - The official Putnam website is: http://math.scu.edu/putnam/index.html. Another very useful web site for problems from some previous years (reworded slightly) and their solutions is: http://web.archive.org/web/20080124125203/www.kalva.demon.co.uk/putnam.html

For more information or to register to participate, contact Prof. Richard Foote (richard.foote@uvm.edu)

]]>The first meeting will be

**Curvature: The Fundamentals**

At the backbone of differential geometry sits the notion of curvature, a quantity measuring how much a curve or surface "curves" at a given point. In this talk, we will introduce the basics of planar differential geometry, including parameterizations of curves, various notions of the curvature vector, and the topology of curves. This talk aims to build a working understanding of curvature with the goal of later applying that knowledge to understanding the mean curvature flow, or curve-shortening flow, of planar curves.

**Origami Knots in Graphs**

Inspired by a potential topological obstruction to the origami method of DNA nanostructure self-assembly design, we define and study origami knots in Eulerian graphs embedded on orientable surfaces in 3-space. We present a complete characterization of origami knots in naturally-defined infinite families of triangular and rectangular toroidal grids, and discuss origami knots in composites of both types of grids embedded on higher-genus surfaces.

]]>Mondays at 6:45 PM

Perkins 101

The Math Club will hold weekly events on Monday evenings at 6:45 PM in Perkins 101 this year. Our **Unofficial Kickoff** will be **Monday, September 5**. We will have opportunities to meet each other and to practice for our next event, the **Faculty vs. Undergrads Math Bee**.

The **Faculty vs. Students Math Bee** will take place on **Monday September 12**. There will be pizza at this event.

Everyone is welcome at all our events, so bring a friend!

We welcome all feedback so if there is anything you want to see become a part of Math Club or you have any questions, email us at mathclub@uvm.edu

]]>Sean Cleary

The City College of New york and the CUNY Graduate Center

Thursday, September 22, 2016

4:30 - 5:30 pm

Kalkin 002

**Abstract:**

Rooted binary trees are an important structure underlying many computational structures, such as binary search trees and more complex data storage methods. Having trees which are relatively balanced is important for having efficient searches. Modifying unbalanced trees to make them more balanced can be done in many ways, including a simple "rotation" operation which is a local move. Rotation distance between trees measures the minimum required number of rotations to transform one tree to another. There are no known efficient algorithms for calculating rotation distance exactly, but there are approximation algorithms. Rotation distance between a pair of trees is equivalent to an edge-flip distance between triangulations of regular polygons. Here, I discuss a number of properties of rotation distances, some of which are easier to recognize from the tree perspective and some from the polygonal perspective. This is based on joint work with Andrew Rechnitzer, Thomas Wong, and Katherine St. John, as well as with undergraduate student researchers at the City College of New York.

ADA: Individuals requiring accommodations please contact Doreen Taylor at 802-656-3166

]]>Samuel V. Scrapino, Ph.D.

Complex Systems

University of Vermont

Thursday, May 5, 2016

4:00 - 5:00 pm

Perkins 101

**Abstract:**

The primary tool for modern population genetic inference is coalescent theory, which provides a retrospective, mathematical framework for relating genetic variation to historical evolutionary processes. Because many pathogens mutate so rapidly, their evolutionary and population-level processes are inextricably linked. Therefore, studying epidemics requires models able to connect evolution to ecology. The emerging field of phylodynamics seeks to leverage the genetic variation of pathogens to investigate their complex, epidemiological dynamics through the use of mathematical transmission models. Linking these models with the genetic sequence data–now routinely collected during disease outbreaks–provides an unprecedented opportunity to advance our scientific understanding of epidemics and pathogen establishment. In this talk, I will present new results on the expected rate of coalescence for diseases spreading through social networks and demonstrate that an unbiased estimate of the coalescent rate can be obtained when only a subset of cases are reported. With these results, we will explore the utility of coalescent models during the 2014-15 ebola outbreak in West Africa and the ongoing whooping cough outbreak in the USA.

ADA: Individuals requiring accommodations please contact Doreen Taylor at (802) 656-3166.

]]>

Monday, May 2, 2016

6:30 PM

Perkins 101

Thanks for a great semester of Math Club! We hope to see at our last meeting of the semester. There will be FREE PIZZA, origami and games.

If you know you will be coming, please contact the Math Club President at rbayersd@uvm.edu so we can get an idea of how many pizzas to order. But if you decide to come at the last minute, that's okay too.

We hope to see you there!

Nick Allgaier, PhD

Postdoctoral Associate in Psychiatry, University of Vermont

Friday, April 29, 2016

4:00 - 5:00 PM

Kalkin 003

**Abstract:**

The neurological mechanisms underlying addiction in humans are still not well understood. Though the reward-based reinforcement learning circuitry of the limbic system has been implicated, it is not clear why many people who partake in recreational drug and alcohol use avoid getting hooked, while others succumb to addiction. In this talk we describe a neurodiagnostic methodology comprised of nonlinear functional mapping (NFM), a procedure developed at UVM for applying an evolutionary algorithm to functional magnetic resonance imaging (fMRI) data, and subsequent classification by support vector machine (SVM). NFM is a symbolic regression algorithm that searches for models relating the activity in different regions of interest (ROI) in the brain, as represented by fMRI signal, without assuming linearity. Summary statistics of the models inferred by NFM indicate levels of pairwise coordination among ROI, and diagnosis of addiction is accomplished by SVM based on these coordination levels.

We apply this methodology to resting-state fMRI time series from a cohort of 25 addicted cigarette smokers, and 30 control subjects. The resulting cross-validated classifier correctly diagnoses all 25 smokers while only miss-diagnosing 5 control subjects. Further, many of the top-ranking SVM features represent coordination among ROI in the prefrontal cortex, as well as coordination between these ROI and both cortical and subcortical ROI involved in the limbic system. The importance of coordination among these particular ROI in addiction diagnosis hints at a mechanism of prefrontal executive control over the limbic system, whose efficacy may be a key determining factor in a subject's risk of addiction.

ADA: Individuals requiring accommodations please contact Doreen Taylor at (802) 656-3166.

]]>**Abstract:** From the right perspective, everything is mathematical – even juggling. In this talk, Greg Warrington from the University of Vermont will describe how juggling relates to traditional mathematical fields such as graph theory and look at what happens when a person starts juggling randomly. In doing so, he’ll illustrate how these mathematical underpinnings can be useful even for accomplished jugglers. There will be numerous live demonstrations with the juggling of 0 to 7 objects.

We hope to see you there!

]]>Mary Beth Ruskai, Emeritus Prof. of Mathematics, University of Massachusetts Lowell

Research Prof., Tufts University

Associate member, Institute for Quantum Computing, Waterlook, Canada

Friday, April 15, 2016, 4:00 PM

Kalkin 003

**Abstract:**

Entanglement is both one of the most puzzling aspects of quantum theory and a key component of powerful new methods of computation and communication. In contrast to classical systems, the conditional information of a quantum system can be negative. It is now known that this can be interpreted in terms of quantum correlations that can be used to transmit information by such mechanisms as quantum teleportation.

In quantum information theory, quantities like mutual and conditional information are defined using the von Neuman entropy. Key properties of the von Neumann entropy are closely associated with operator and trace inequalities, which can be proved using extremely elementary methods.

This talk will give an overview of, and introduction to, the concepts mentioned above. No prior knowledge of quantum theory is required and the mathematics is accessible to anyone with a good knowledge of linear algebra.

]]>

Generalizations and Applications

Sagun Chanillo, Rutgers University

Friday, April 8, 2016, 4:00 PM

Kalkin 004

**Abstract:**

The Fundamental theorem of Calculus can be generalized in two ways in higher dimensions, via the Gagliardo-Nirenberg inequality with its close connections to the isoperimetric inequality and the Moser-Trudinger inequality which has powerful ramifications in Conformal Geometry. Recently a third inequality was discovered by Bourgain-Brezis which is very close to the fundamental theorem of Calculus in one dimension. We discuss generalizations of this inequality to Nilpotent Lie Groups, Riemannian Symmetric spaces and also a new proof of the original inequality of Bourgain-Brezis that allows us to extend the scope of the Bourgain-Brezis inequality. Lastly we provide appliactions of the Bourgain-Brezis inequality to the two dimensional Navier-Stokes equation of Fluid Mechanics and the Maxwell equations of Electromagnetism. This is joint work with Jean Van Schaftingen and Po-lam Yung.

]]>

A panel Discussion with UVM Alumni and Community Professionals

Jeffrey Young,

Brian Orleans,

John Stanton-Geddes,

Polly Ramsey,

Leah Shulman,

Wednesday, April 6, 2016, 7:00 - 8:15 pm

Waterman Memorial Lounge

The UVM Statistics program will host a panel presentation of careers in Statistics and Data Science on Wednesday, April 6 from 7:00 - 8:15 pm in Waterman Memorial Lounge. Five speakers will talk about career opportunities at Dealer.com, ICF International, Cigna Insurance, and the Vermont Health Department. A question and answer session will follow. Refreshments will be served.

Save the date for the last few meetings of the semester:

April 2 - Hudson River Undergraduate Math Conference at Saint Michael's College

April 4 - Jim Bozeman's talk on gerrymandering

April 18 - Greg Warrington's talk

May 2 - End of year celebration

]]>We will be building a modular origami creation as well as playing games such as Set.

Feel free to bring your favorite board game to play. We will provide some as well.

All are welcome. Bring a friend!

]]>**When:** Thursday, February 4, 2016, 12:00 - 1:00 PM

**Place:** Math Conference Room

Bring your lunch.

**Speaker:** Ian M. Wanless, Monash University

**Title:** *Embedding small partial Latin squares in Cayley tables*

**Abstract:**

Sudoku puzzles are examples of a combinatorial object called a partial latin square (PLS). In 1974 Keedwell asked for each n what is the smallest PLS that cannot embed into any group table of order n. In 2012 Hirsch and Jackson asked what is the smallest PLS that can be embedded in an infinite group but not into any finite group. We answer both these questions and a couple of related ones.