We will discuss **sections 1 and 2** of the paper *Stratification and weighting via the propensity score in estimation of causal treatment effects: a comparative study *(attached).

There are some technical passages in Section 2, but the paper provides a clear introduction and review of propensity scores, which are widely used to estimate causal treatment effects from observational studies.

Pizza will be served.

SUMMARY

"Estimation of treatment eects with causal interpretation from observational data is complicated because

exposure to treatment may be confounded with subject characteristics. The propensity score, the

probability of treatment exposure conditional on covariates, is the basis for two approaches to adjusting

for confounding: methods based on stratication of observations by quantiles of estimated propensity

scores and methods based on weighting observations by the inverse of estimated propensity scores. We

review popular versions of these approaches and related methods oering improved precision, describe

theoretical properties and highlight their implications for practice, and present extensive comparisons of

performance that provide guidance for practical use. Copyright ? 2004 John Wiley & Sons, Ltd."

Join us once more for a riveting math competition where students and faculty fight to bring home the coveted Golden Pi trophy! All answers are team-based, no one will be put on the spot.

Pizza and soda will be served, and students of all majors and math levels are welcome!"

]]>Math Club will be having our first general meeting

Next week, we will be having our first event of the semester: The Math Bee! This is where students and faculty go head-to-head in a math competition to bring home the coveted Golden Pi trophy! This will be during our normal meeting time on Monday, the 29th.

All majors and math levels are welcome!

Hope to see you there,

Jack Felag

Math Club President

Regular Math Club Meetings will be held every Monday from 6:30-8:30 in Perkins 101.

]]>The annual Altmetric Top 100 ranks which pieces of research have caught the public imagination in the last 12 months. To determine 2017’s list, Altmetric tracked over 18.5 million mentions of 2.2 million different pieces of research.

The study by UVM professor Chris Danforth and Andrew Reece of Harvard University, “Instagram photos reveal predictive markers of depression,” came in at No. 17. Danforth is a professor in UVM's Department of Mathematics & Statistics and co-director of the university's Computational Story Lab.

Published Aug. 8 in a leading data-science journal *EPJ Data Science*, the research was covered by media outlets around the world including *The New York Times*, *USA Today*, *Quartz*, and nearly 250 others. The study was also mentioned in thousands of tweets, blog posts, and more.

“As in previous years, medical and public health issues have drawn the highest levels of attention,” according to Almetric’s website.

Read more about Danforth’s findings, and view the full Altmetric Top 100 ranking.

]]>

While the session will focus on mathematics and statistics, the information should be applicable to a wide range of technical subjects, so do not hesitate to come even if you are a CS or engineering major, or any major in STEM! (So bring a friend!)

It will be especially useful for first years and sophomores to attend; laying the groundwork for strong applications to research opportunities takes time and planning. It’s never too early to consider the next step.

Finally, if you are a junior or senior and you have done an REU or other research experience, please come to share your experience with others.

This information will take place on Wednesday December 6, starting at 5:15pm, in Perkins 102.

Hope to see you there,

Jack Felag

Math Club President

Dr. Anna Haensch

Assistant Professor

Department of Mathematics and Computer Science Duquesne University

Friday, December 1st, 4:30PM Kalkin – Room 002

Abstract: A rational polynomial f(x) is solvable if f(x)=0 has an integer solution. Hilbert’s 10th problem famously asks whether there is a general finite algorithm to determine whether a polynomial is solvable. From work completed in the 1960’s we know that the answer to Hilbert’s 10th problem is a definitive ``no.” However, if we restrict to certain types of polynomials the answer becomes ``yes.” In this talk we will explore linear, quadratic, and higher degree polynomials in the context of the solvability problem and we will look at some classical results in this area. We will discuss some familiar techniques like the Euclidean algorithm and the quadratic equation, and perhaps some less familiar techniques involving quadratic lattices and modular forms. Eventually we will land in the realm of cutting edge research problems in solvability for quadratic polynomials. This talk will be aimed at advanced undergraduate students, graduate students, and anyone with an inclination towards number theory.

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

REFRESHMENTS WILL BE SERVED.

]]>This Friday we will be discussing Reproducibility and Null Hypothesis Testing.

....PIZZA WILL BE SERVED....

]]>

Christopher Purcell

Aalto University - Finland

Friday, November 17th, 4:30PM

Kalkin – Room 001

Abstract:

The famous theorem of Robertson and Seymour states that graphs are well-quasi-ordered by the minor

relation. This tells us that every minor-closed graph class can be characterized by a finite list

of minimal forbidden minors. As a result, every set of minor-closed graph classes has a minimal

element under the containment relation. Thus, we may characterize a family of minor- closed classes

by listing the minimal classes outside the family. Characterizing families of classes closed under

vertex deletion (hereditary classes) is more challenging. Since graphs are not well-quasi-ordered

by the induced subgraph relation, there need not be a minimal element of a set of hereditary

classes in general. To overcome this difficulty, new machinery was developed which will be

described in this talk. We will give an overview of the main results and techniques, and of the

applications to computational complexity and other areas. This talk will be accessible to graduate

students in mathematics and computer science.

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

REFRESHMENTS WILL BE SERVED.

]]>Department of Mathematics & Statistics

UVM and University Scholar

Day and time: Monday, November 13, 4:30 - 5:30 pm.

Location: 223 Votey

Title: All-real spectra in optical systems with arbitrary gain-and-loss distributions

Abstract

A method for constructing optical potentials with an arbitrary distribution of gain and loss and completely real spectrum is presented.

For each arbitrary distribution of gain and loss, several classes of refractive-index profiles with freely tunable parameters are obtained

such that the resulting complex potentials, although being non-parity-time-symmetric in general, still feature all-real spectra for a wide range of parameters.

Under parameter tuning in these potentials, a phase transition can also occur, where pairs of complex eigenvalues appear in the spectrum. In some classes of these potentials, a distinctive feature of the phase transition is that the complex eigenvalues may bifurcate out from an interior continuous eigenvalue inside the continuous spectrum. These non-parity-time-symmetric complex potentials generalize the concept of parity-time-symmetric potentials to allow for more flexible gain-and-loss distributions while still maintaining all-real spectra and the phenomenon of phase transition.]]>

Wednesday, November 1, 2017 at 5:15PM

Perkins 102

PIZZA WILL BE SERVED!

The UVM Math Club will be hosting a Course Review Night this coming Wednesday November 1st.

It is a FACULTY FREE event to dicuss courses, akin to an advising session, but with a student's perspective on a class is structured.

This review will be especially helpful for underclassmen who need help with scheduling.

We hope to see you there!

]]>** **

Professor Richard O. Moore

Department of Mathematical Sciences

New Jersey Institute of Technology

Friday, October 27th, 4:30 PM

Kalkin 001

** **

**Abstract: **

The ability to compute probabilities of rare events is of critical importance in several physical settings, ranging from chemical reactions to magnetic memory devices. Importance sampling using closed- or open-loop feedback based on maximum likelihood paths has been demonstrated to improve the efficiency of Monte Carlo estimation of such probabilities by several orders of magnitude, even when the maximum likelihood paths are determined from an approximate model of low dimension. We demonstrate this approach using examples taken from fiber-optic communications, mode-locked lasers, and magnetoresistive memory.

We show how careful observation of the biased dynamics can suggest improvements to the low-dimensional model that can, in turn, be fed back into new biased simulations of the full model.

]]>

**application to HPV infection dynamics from couple cohort studies **

** **

Xiangrong Kong, PhD

Assistant Professor

Department of Biostatistics and Epidemiology

UMass-Amherst School of Public Health and Health Sciences

**Wednesday, November 15th, 4:00 PM Waterman - 458**

** **

**Abstract:**

We consider a specific situation of correlated data where multiple binary outcomes are repeatedly measured on each member within a couple. Such multivariate longitudinal data from couples generate multi-faceted correlations which can be further complicated if there are polygamous partnerships. An example is data from cohort studies on human papilloma virus (HPV) transmission dynamics in heterosexual couples. HPV is a common sexually transmitted disease with 14 known oncogenic types causing anogenital cancers. The binary outcomes on the multiple types measured in couples over time introduce inter-type, intra-couple, and temporal correlations. Simple analysis using generalized estimating equations or random effects model lacks interpretability and cannot fully utilize the available information. We develop a hybrid modeling strategy using Markov transition technique together with pairwise composite likelihood for analysis of such data. The method can be used to identify risk factors associated with HPV transmission and persistence, estimate difference in risks between male-to-female and female-to-male HPV transmission, compare type-specific transmission risks within couples, and characterize the inter-type and intra-couple associations. Applying the method to HPV couple data collected in a Ugandan male circumcision (MC) trial, we assess the effect of MC and role of gender on risks of HPV transmission and persistence.

Time permitting, another topic on evaluation of the population impact of HIV prevention programs (such MC scale-up) on the HIV epidemic in Uganda will also be introduced to showcase how biostatistical skills are applied in addressing important public health questions.

]]>**Join us this Friday the 13th at 12:00!**

Tufts University

Kalkin 001

**Abstract:**

Prime numbers are often said to be ``random'', but, given that primes are deterministic, what does that actually mean? One way in which this randomness manifests is in the last digits of primes: it turns out that each possible last digit is equally likely in a certain strong sense. A similar story holds for the residue class of primes modulo any fixed integer, and this is a well-understood classical theorem of analytic number theory. Surprisingly, however, in joint work with K. Soundararajan, we find that an analogous phenomenon does not hold for patterns of consecutive primes. For example, a string of consecutive primes ending in the digit 1 strongly predisposes the following prime to not end in a 1; thus, prime numbers are subject to the gambler's fallacy. This talk will be aimed at the level of graduate students and non-experts, but should be satisfying to practicing number theorists as well.

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

]]>College of Optical Sciences

Arizona Center for Mathematical Sciences

University of Arizona

Thursday, Septemter 21, 2017 at 4:30 PM

Decision Theater

**Abstract:**

We have identified major paradigm shifts relative to near-IR filamemtation when high power multiple terawatt laser pulses are propagated at mid-IR and long-IR wavelengths within key atmospheric transmission windows. Individual filaments at near-IR (800nm) wavelengths typically persist only over tens of centimeters, despite the whole beam supporting them being sustained over about a Rayleigh range. In the important mid-IR atmospheric window (3.2-4 µm) optical carrier wave self-steepening (carrier shocks) tend to dominate and modify the onset of long range filaments. These shocks generate bursts of higher harmonic dispersive waves that constrain the intensity growth of a filament to well below the traditional ionization limit, making long range low loss propagation possible. For long wave pulses in the 8-12 µm atmospheric transmission window, many electron dephasing collisions from separate gas species acts to dynamically suppress the traditional Kerr self-focusing lens action and leads to a new type of whole beam self-trapping over multiple Rayleigh ranges. This prediction is key as strong linear diffraction at these wavelengths is a major problem and normally requires large launch beam apertures.

I will review our continuing work in this area and will also discuss some recent efforts to extend the HITRAN linear atmospheric transmission/refractive index database to include nonlinear responses of important atmospheric molecular constituents.

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

]]>Perkins 102

**PIZZA WILL BE SERVED!**

Please join us for the first Math Club meeting of the semester! We will spend the first half hour or so introducing ourselves to each other and welcoming new Math Club members. After the introductions, we will hold our semi-annual Math Bee, where students and faculty go head to head in a friendly mathematics trivia competition and compete for the coveted Golden Pi trophy. All skill levels and majors are invited, so bring a friend!

We hope to see you there!

]]>That's the conclusion of new research showing that computers, applying machine learning, can successfully detect depressed people from clues in their Instagram photos. The computer's detection rate of 70 percent is more reliable than the 42 percent success rate of general-practice doctors diagnosing depression in-person.

"This points toward a new method for early screening of depression and other emerging mental illnesses," says Chris Danforth, a professor at the University of Vermont who co-led the new study with Andrew Reece of Harvard University. "This algorithm can sometimes detect depression before a clinical diagnosis is made."

The team's results were published Aug. 8 in a leading data-science journal *EPJ Data Science*—and have been followed by media stories in outlets around the world including *The New York Times*, *USA Today*, *Quartz*, and hundreds of others.

The scientists asked volunteers, recruited from Amazon's Mechanical Turk, to share their Instagram feed as well as their mental health history. From 166 people, they collected 43,950 photos. The study was designed so that about half of the participants reported having been clinically depressed in the last three years.

Then they analyzed these photos, using insights from well-established psychology research, about people's preferences for brightness, color, and shading. "Pixel analysis of the photos in our dataset revealed that depressed individuals in our sample tended to post photos that were, on average, bluer, darker, and grayer than those posted by healthy individuals," Danforth and Reece write in a blog post to accompany their new study. They also found that healthy individuals chose Instagram filters, like Valencia, that gave their photos a warmer brighter tone. Among depressed people the most popular filter was Inkwell, making the photo black-and-white.

"In other words, people suffering from depression were more likely to favor a filter that literally drained all the color out the images they wanted to share," the scientists write.

Faces in photos also turned out to provide signals about depression. The researchers found that depressed people were more likely than healthy people to post a photo with people's faces—but these photos had fewer faces on average than the healthy people's Instagram feeds. "Fewer faces may be an oblique indicator that depressed users interact in smaller settings," Danforth and Reece note, which corresponds to other research linking depression to reduced social interaction—or it could be that depressed people take many self-portraits.

"This 'sad-selfie' hypothesis remains untested," they write.

As part of the new study, Danforth and Reece had volunteers attempt to distinguish between Instagram posts made by depressed people versus healthy. They could, but not as effectively as the statistical computer model—and the human ratings had little or no correlation with the features of the photos detected by the computer. "Obviously you know your friends better than a computer," says Chris Danforth, a professor in UVM's Department of Mathematics & Statistics and co-director of the university's Computational Story Lab, "but you might not, as a person casually flipping through Instagram, be as good at detecting depression as you think."

Consider that more than half of a general practitioners' depression diagnoses are false—a very expensive health care problem—while the computational algorithm did far better. The new study also shows that the computer model was able to detect signs of depression before a person's date of diagnosis. "This could help you get to a doctor sooner," Danforth says. "Or, imagine that you can go to doctor and push a button to let an algorithm read your social media history as part of the exam."

As the world of machine learning and artificial intelligence expands into many areas of life, there are deep ethical questions and privacy concerns. "We have a lot of thinking to do about the morality of machines," Danforth says. "So much is encoded in our digital footprint. Clever artificial intelligence will be able to find signals, especially for something like mental illness." He thinks that this type of application may hold great promise for helping people early in the onset of mental illness, avoid false diagnoses, and offer a new lower-cost screening for mental health services, especially for those who might not otherwise have access to a trained expert, like a psychiatrist.

"This study is not yet a diagnostic test, not by a long shot," says Danforth, "but it is a proof of concept of a new way to help people."

]]>1986, nine-year-old Zack Scott fell for America’s game and Boston’s team. If you’re a Red Sox fan, you know, *that* season. Up three games to two versus the New York Mets in the World Series, the tenth inning slow roller off Mookie Wilson’s bat skips between poor, pilloried Bill Buckner’s legs, the Mets’ winning run crosses home, Red Sox dreams of ending The Curse melt with game six and seven heartbreakers, on hold for another eighteen years.

So, Scott ’99, the Sox’ head analytics guy, VP for baseball research and development, found the game and the team that would one day be his calling with a season that, to large degree, hinged on a play that defied the odds. Buckner would make that play, what, 99 out of 100 times? In a game of cruel inches, crazy bounces, and mortal rotator cuffs, so it goes. But years later, pioneering front office leaders would begin to realize that close, objective examination of the myriad statistics of baseball could yield better results on the field. There’s no inoculation against chance. But enlisting the reasoned as another line of defense against the random is akin to adding a tenth player named “Evidence-Based Decision-Making” to the lineup.

Today, sabermetrics, the empirical analysis of baseball statistics, is a critical dimension of Major League Baseball front office work, and the Red Sox are among the teams with notable investment and success on this front. As a *Boston Herald* pre-season article described Zack Scott’s role: “There is no one more vital to the future of the Red Sox…”

It’s the 2017 season-opening series at Fenway Park. But as a quaintly New England brew of cold, wind, and rain lashes the city, the day game is called. The concession stands on Yawkey Way are shuttered—no Luis Tiant Cubano for you. Fans console themselves browsing the seemingly infinite variations on Red Sox caps for sale at the official store across the street. Out-of-towners wearing Pirates jerseys and forlorn faces head to the refuge of Back Bay shopping malls.

But through a side door off Yawkey, up a few flights of stairs, the work of the Boston Red Sox front office quietly hums along. Zack Scott’s office is spare and windowless, buried somewhere in the sprawl of Fenway along the third base line. Past success, a huge photo of the 2007 World Champions banner being unfurled on a blue-sky opening day 2008, hangs on the wall behind his desk. Present and future is in full view on the opposite wall. A white board displays the 2017 game schedule, and the names of players on the active roster, optioned, and 10-Day Disabled List in three tidy columns.

A small corner bookshelf holds pictures of Scott’s wife, Molly, their two kids, Zoe, six, and Perry, three; a bright splash of kid’s art; and dense stacks of baseball stats and analytics books. Among the volumes, works by Bill James, godfather of sabermetrics and a consultant to the Red Sox. The wonkish world of baseball statistics had its spotlight moment with Michael Lewis’s 2003 bestseller *Moneyball*, the story of Oakland Athletics’ general manager Billy Beane’s quest to leverage innovative analytics and turn a cash-poor team into a winner. The book vaulted the work of Beane, his assistant Paul DePodesta, and the pioneering James into the public consciousness. Scott says that, to some extent, he and colleagues in the field owe their careers to *Moneyball*. The book opened eyes and eventually doors in pro baseball’s front offices.

Over fifty participants from all over the Americas and Europe will spend the week at University Heights South developing open source mathematical software to facilitate computations with p-adics numbers and updating and developing the L-functions and modular forms database. Beginners are welcome and there will be a mini-bootcamp for novices on the first afternoon of the workshop.

For more information, please see the Sage Days wiki page.

]]> **Please describe the basic elements of your data science/analytics curriculum and how the curriculum was developed.**

Our program provides students with a transdisciplinary education that prepares them for business environments or a PhD in an analytic field. Our program is more scientific than professional and is unique in its combination of complex systems and data science (CSDS). Throughout the MS in CSDS program, students are challenged to create defensible arguments for their findings, with warnings against the many potential pitfalls associated with exploring large-scale data sets, coupled with the use of computational process-based models that lend insight into emergent properties of complex systems. Admissions requirements include courses in calculus, programming, data structures, linear algebra, and probability and statistics. We offer opportunities for students to make up missing prerequisites.

**Year in which the first students graduated/are expected to graduate: **2016**Number of students currently enrolled:** Five**Partnering departments:** Department of Mathematics and Statistics, Department of Computer Science**Program format:** In-person instruction, 30 credits (coursework only, project, and thesis options). Support for finding internships, no graduate teaching assistantships, research assistantships possible for students working with externally funded advisers.

**What was your primary motivation(s) for developing a master’s data science/analytics program? What’s been the reaction from students so far?**

Almost all scientific fields have moved from data scarce to data rich, and sophisticated analyses have been made possible by the advent of distributed computing and storage, with accompanying advances in algorithms and theory. As Big Data has become a common thread across disparate disciplines, so too have methods for contending with the many difficulties presented by large-scale data analysis. The program was created to address the opportunities created by these conditions. Faculty were already working on modeling and analysis of complex systems using transdisciplinary approaches, and we already had a five-course Certificate of Graduate Study in Complex Systems, so it was natural to build an MS degree upon this foundation.

Quote from a student course evaluation: “This class changed the way I see the world.”

**How do you view the relationship between statistics and data science/analytics?**

Data science is at the intersection of statistics and computer science. Data munging, machine learning, visualization, text processing, heterogeneous data types, and web scraping are examples of tasks not typically addressed in traditional statistics programs. Inferential logic/methodologies and design of experiments are not typically taught in computer science programs. A large number of schools have business-themed data science programs. The core data science part of our MS in CSDS at UVM provides more general purpose training, though certainly a career in the business world would be a possible outcome for students.

**What types of jobs are you preparing your graduates for? **

We have developed close relationships with several companies, and they are helping to support our programs. The program is new and we don’t yet have data to address demand for our graduates, but it is worth noting that data scientists are increasingly in demand across the spectrum of occupations in government, finance, corporations, and journalism. The job title of data scientist is now commonplace. Popularized by Nate Silver and *Moneyball*, training in data science is being sought after across the United States. Perhaps the clearest evidence is the growth of data science degrees globally. Also, these degrees, which are largely master’s level, are easily being filled by applicants within the United States.

**What advice do you have for students considering a data science/analytics degree?**

We aim to serve students coming from a wide variety of backgrounds and therefore deliberately keep the prerequisites to a minimum. Students must have a bachelor’s degree in a relevant field and prior coursework in computer programming, data structures, calculus, linear algebra, probability, and statistics.

Our program is ideal for students interested in the intersection of statistics, computer science, and mathematics with applications in any of a wide variety of domains. The degree provides more exposure to computing and statistics than the traditional statistics or computer science degrees (respectively), offers unique transdisciplinary courses in complex systems and data science, does not require strictly disciplinary courses (e.g., we do not require computer science–specific courses like operating systems), and provides a great deal of flexibility in customizing coursework to student interests.

**Do you have any advice for institutions considering the establishment of such a degree?**

The statistics, computer science, and mathematics programs at UVM have a collegial relationship, which has helped significantly in the formation of our BS in data science and our MS in complex systems and data science degrees. We work closely on course scheduling so the courses in the different disciplines do not conflict. Cross-listing of courses also provides for increased options for students. Collaboration is also made easier in that the participating disciplines all reside in the College of Engineering and Mathematical Sciences.

is an assistant professor of mathematics and statistics at the University of Vermont and a member of the Vermont Complex Systems Center. He has degrees in liberal arts (AS) and physics (BS, MS, and PhD).

James P. Bagrow

Jeffrey S. Buzasis professor and chair of mathematics and statistics and director of the statistics program at the University of Vermont. He has degrees in mathematics (BS) and statistics (MS and PhD).

Peter Sheridan Doddsis a professor in mathematics and statistics at the University of Vermont, where he is also the director of the Vermont Complex Systems Center and co-director of the Computational Story Lab.

Margaret J. Eppsteinis professor and chair of computer science at the University of Vermont and founding director of the Vermont Complex Systems Center. She has a BS in zoology, MS in computer science, and PhD in environmental engineering.

]]>

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

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!

]]>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

]]>