Bard Assistant Professor of Mathematics Matthew Junge Talks with WAMC about National Science Foundation RAPID Grant to Study COVID-19 Forecasting Models

“What’s really distinguishing [our study} from a lot of the studies that are being quoted by the national press . . . and the Administration is that we look at the local connections inside of communities, and those are usually ignored by bigger studies,” Junge tells WAMC’s Hudson Valley Bureau Chief Allison Dunne.

Bard Assistant Professor of Mathematics Matthew Junge Talks with WAMC about National Science Foundation RAPID Grant to Study COVID-19 Forecasting Models

“What’s really distinguishing [our study} from a lot of the studies that are being quoted by the national press . . . and the Administration is that we look at the local connections inside of communities, and those are usually ignored by bigger studies,” Junge tells WAMC’s Hudson Valley Bureau Chief Allison Dunne. “Our study’s taking this opposite perspective of really finally modelling person-to-person connections that come up in our day-to-day lives, like who we socialize with, where we work, connections of that sort, and we ask how the disease spreads in this sort of zoomed-in picture.”

The National Science Foundation (NSF) has awarded Bard College professors Matthew Junge, mathematics, and Felicia Keesing, biology; and Grinnell College professor Nicole Eikmeier, computer science, a $60,000 grant to develop network models that better capture the geographic and social complexity of the COVID-19 pandemic. The NSF’s Rapid Response Research (RAPID) program provides support for urgent scientific research that responds to emergencies and unexpected events.

Bard College Professors Win National Science Foundation Rapid Grant to Develop Forecasting Models that Better Capture the Geographic and Social Complexity of the COVID-19 Pandemic

The National Science Foundation (NSF) has awarded Bard College professors Matthew Junge, mathematics, and Felicia Keesing, biology; and Grinnell College professor Nicole Eikmeier, computer science, a $60,000 grant to develop network models that—by more accurately incorporating social distancing measures—better capture the geographic and social complexity of the COVID-19 pandemic. Awarded through the NSF’s Rapid Response Research (RAPID) program, which provides support for urgent scientific research that responds to emergencies and unexpected events, the grant includes funding for salaries, publishing costs, and several undergraduate research assistants over a six-month period.

Junge, Bard assistant professor of mathematics and lead investigator on the project, says their project aims to develop network models and mathematical theory to test the robustness of some prominent models being used by governments to justify the extreme levels of intervention we are living through. One advantage of a network model, which tries to accurately describe the face-to-face interactions each individual in a society has and how an infection might spread, is that it is relatively easy to implement social distancing into the network.

“Mathematicians are fairly adept at modeling the natural evolution of epidemics, but most ‘off the shelf’ models were not built to describe the dramatic levels of intervention—business closures, travel limitations, and social distancing—that we are living through during the COVID-19 pandemic,” says Junge. “The grant brings together a biologist (Felicia), computer scientist (Nicole), and mathematician (myself) as well as a few undergrad research assistants to tackle this problem over the next six months. Felicia is an expert in infectious disease, Nicole in modeling real world networks, and I am experienced in network infection models.”

Matthew Junge, assistant professor of mathematics, comes to Bard from Duke University, where he served as William W. Elliott Research Assistant Professor. He received his doctorate in mathematics from the University of Washington, where he also earned MS, BS, and BA degrees. His areas of interest include probability, statistical physics, and mathematical biology. Junge’s research takes a probabilistic approach to particle systems from physics and biology, including models for chemical reactions, species proliferation, and epidemic outbreaks. He also studies random structures from classical mathematics and computer science, such as permutations and fragmented spaces.

Felicia Keesing, David and Rosalie Rose Distinguished Professor of Science, Mathematics, and Computing, has been on the Bard faculty since 2000. She has a B.S. from Stanford University and a Ph.D. from the University of California, Berkeley. Since 1995, she has studied how African savannas function when the large, charismatic animals like elephants, buffaloes, zebras, and giraffes disappear. She also studies how interactions among species influence the probability that humans will be exposed to infectious diseases. Keesing also studies Lyme disease, another tick-borne disease. She is particularly interested in how species diversity affects disease transmission.

Nicole Elkmeier is an assistant professor of computer science at Grinnell College. She has a PhD in Mathematics from Purdue University and a BA from in mathematics and computer science from Concordia College. Her research is in the field of Network Analysis, specifically focused on studying features of real data and constructing and analyzing graph models which maintain those features. A network, in this case, is a set of nodes (people, web pages, etc.) connected by edges (physical connection, collaboration, etc). She is interested in random graph models, which are used to study how well an algorithm may do on a real-world network, and for testing properties that may further improve algorithms. Her research is at the intersection of math and computer science.

Kate Belin BA ’04, MAT ’05 teaches math at Fannie Lou Hamer Freedom High School, a small public school in the South Bronx that uses project-based learning. At Fannie Lou, she oversees the Algebra Project, a national initiative that connects math to students’ lived experiences.

The Algebra Project: Bard Alumna, Teacher Kate Belin on Using Math to Help Students Build More Ethical Communities

Kate Belin BA ’04, MAT ’05 teaches math at Fannie Lou Hamer Freedom High School, a small public school in the South Bronx that uses project-based learning. At Fannie Lou, she oversees the Algebra Project, a national initiative that connects math to students’ lived experiences. In this episode of the Ethical Schools podcast, Belin talks about the synergy between the Algebra Project and Fannie Lou, both of which have their roots in the history of the civil rights movement.

Mathematics Professor Matthew Junge Receives National Science Foundation Grant

Matthew Junge, Bard College Assistant Professor of Mathematics, has been awarded a grant from the National Science Foundation in the amount of $190,868 for research into multitype particle systems. The grant comes from the NSF's Division of Mathematical Sciences Probability Program.

Interacting particle systems with random dynamics are fundamental for modeling phenomena in the physical and social sciences. Such systems can be used to describe chemical reactions, as well as the spread of disease, information, and species through a network. These models often become more meaningful when multiple particle types are incorporated. For example, the celebrated First Passage Percolation model describes the spread of a single species through an environment; the incorporation of competing species enriches the model. This project seeks to study more realistic variants of well-known models for chemical reactions, epidemic outbreaks, and the spread of information as to deepen our understanding of important phenomena from across the sciences and further develop the mathematics that helps explain them. The project will involve the training of undergraduate students.

In summer 2020, Professor Junge will use a portion of the NSF grant to run a Tiny Mathematics Research Community at Bard that vertically connects undergraduates, graduates, postdoctoral researchers, and professors in a retreat-style research workshop.

Professor Junge joined the Bard faculty this fall, coming to Annandale from Duke University, where he served as William W. Elliott Research Assistant Professor of Mathematics. He received his doctorate in mathematics from the University of Washington, where he also earned MS, BS, and BA degrees.

His areas of interest include probability, statistical physics, and mathematical biology. Professor Junge’s research takes a probabilistic approach to particle systems from physics and biology, including models for chemical reactions, species proliferation, and epidemic outbreaks. He also studies random structures from classical mathematics and computer science, such as permutations and fragmented spaces.

This semester, he is teaching Probability and Calculus I, as well as supervising a research project with two Bard undergraduate students. He also teaches in the Bard Prison Initiative, alongside Mathematics Program colleagues John Cullinan and Japheth Wood.

STEAM Explorers: Changing How Kids Think About Science and Math

By Sarah Wallock ’19

If you’re passing through the Reem-Kayden Center on a given Saturday afternoon, you may run into a group of middle school girls, chatting about math games and examining the origami designs that they just made in the Girls Math Club. Or, if you’re a patron of the Tivoli Library, you may come across a STEAM Workshop using soap and food coloring to make marbled milk paper and learn about how calcium affects saturation rates. Both programs are hosted by STEAM Explorers, an initiative of Bard’s Center for Civic Engagement (CCE) and Math Program. STEAM Explorers has two components: Bard Science Outreach and the Bard Math Circle. Together, they work to create experiences and design experiments that inspire wonder, spark curiosity, and challenge old ideas.

Sarah deVeer ’17 volunteered for STEAM Explorers as a Bard student; now, she runs the program as the science outreach coordinator. This year she has worked to expand the program beyond local partners in Red Hook, Rhinebeck, Kingston, and Tivoli to communities across the Hudson Valley such as in Beacon, Albany, and Hudson. Sarah also worked to revamp the curriculum, and to good effect: John Kemnitzer, the principal of Bulkeley Middle School in Rhinebeck, recently said that this year’s program was the best one yet.

Children participating in Bard’s STEAM Explorers program make marbled milk paper at the Tivoli Library. Photo by Sarah Wallock ’19.

“One aspect that I really love about Bard’s STEAM Explorers is that we don’t charge the schools or community for our programs,” says deVeer. “We offer these programs because we genuinely believe that Bard is a private institution operating in the public interest.” Working with six STEM fellows and 30 engagement mentors, STEAM Explorers collaborates with 12 partners in schools and community organizations throughout the Hudson Valley. DeVeer also coordinates science engagement efforts as part of Bard’s Citizen Science Program and Martin Luther King Jr. Day of Engagement. The most important part of discussing issues such as water quality and natural resource use with students, she notes, is how STEAM Explorers is “starting the conversation with the next generation.”

The Bard Math Circle was started in 2007 by mathematics students and faculty at Bard, to address the dearth of math enrichment opportunities in the Mid-Hudson Valley. It began with a monthly program at the Tivoli library, where the organizers brought puzzles, games, and toys that emphasized problem-solving skills and making math fun for all ages. Students attending the library programs reported doing better in their math courses at school because of their involvement with the project.

The Girls Math Club, led by Bard students, works on origami designs in the Reem-Kayden Center on Bard’s campus. Photo by Bari Bossis ’19.

From the outset, Bard undergraduates have been an integral part of the Math Circle, running and developing programs, leading hands-on workshops, and mentoring K-12 students. The Math Circle has expanded over time to include programs at several libraries, schools, and community centers; math contests and national math competitions; programs to empower girls in math; a Rubik’s Cube Club; special events for teachers and senior citizens; and the most popular program, a weeklong summer CAMP (Creative, Analytical Math Program) for middle schoolers, run primarily by Bard faculty, alumni/ae, undergraduates, and local high school volunteers who have taken part in Math Circle programs. One parent whose daughter participated in the Girls Math Club recently commented, “My child was always happy after meetings, and she liked the girls-only space to learn and explore.” Undergraduate leaders credit their involvement with the Math Circle as one of the highlights of their Bard experience. The majority of Math Circle student leaders choose to pursue a career in teaching after graduation.

STEAM Explorers started in 2010 as an effort to bring science and math to area students in new and creative ways. Bard Science Outreach fellows and Bard Math Circle faculty and volunteers work with more than 4,000 children and teens throughout the Hudson Valley each year. Partnering with local schools, they connect what students are learning in the classroom with real-world issues, especially those facing the Hudson Valley region.

During the month of January, Science Outreach fellows worked with six different school districts to host a Day of Science. The CCE outreach team conducted science experiments around the theme of Hudson River watershed health, from off-campus events at Chancellor Elementary in Rhinebeck and Smith Intermediate School in Hudson, to on-campus events for local middle school students. Bard students led activities that showed the importance of local aquifers to the ecosystem. Participants tested the salinity of the river water, played a PCB board game, explored pH filters, and demonstrated water conservation through interactive activities.

STEAM Explorers works to provide real-world applications in all its experiments, like dissecting owl pellets to classify rodent skeletons and building marshmallow towers to learn effective design and construction mechanisms. “My favorite experiment was when we played with owl pellets!” says Junnaria, a sixth-grade student in Perfect Ten, an after-school program in Hudson that empowers and mentors young girls. “It was so cool finding all the bones of the animals! This [experiment] has made me more curious about nature and biology.” Melissa, a seventh grader from Perfect Ten, comments, “I really liked the marshmallow tower. It showed me how to plan measurements for buildings. It’s cool to find out that math and science are in everything, even marshmallows.”

Antonio Gansley-Ortiz ’18, a science outreach engagement mentor, reflects on how his work with the STEAM Explorers continues to influence him: “In April while out having dinner with [another mentor], I ran into one of my middle school students. She recognized us and pointed us out to her parents. The entire family then came over and thanked us for the experience. They also mentioned the student hadn’t stopped talking about her excitement with science. That moment was incredibly fulfilling. I want to help provide that positive experience to other students in the community.”

STEAM Explorers Initiatives

Day of Science brings eighth graders from local school districts to the Bard campus to engage with Bard science fellows, faculty, and undergraduates in a series of themed science stations.

Girls Math Club for middle school girls run by Bard female math majors.

Math Circle Library Programs include puzzles, games, and fun math activities for upper elementary and middle school students.

Rubik’s Cube Club teaches kids how to master the Rubik’s Cube.

Science Fairs connect Black Student Organization fellows and volunteers to mentor local students preparing to enter school science fairs.

Science for Kids brings in-school, hands-on science experiments to K-5 students by using household products in new ways.

Science Saturday brings children and families together with Bard students at local libraries and community centers to participate in science enrichment activities.

STEM Night Out invites young students throughout the Hudson Valley to an evening of fun, hands-on scientific experiments led by science fellows and Bard first-year students.

Bard College Students Telo Hoy ’19 and Meagan Kenney ’19 Awarded U.S. Department of State’s Benjamin A. Gilman International Scholarship to Study Abroad

Bard College students Telo Hoy and Meagan Kenney have been awarded Benjamin A. Gilman International Scholarships to study abroad for the fall 2017 semester. Hoy, a music composition major from Santa Fe, New Mexico, was awarded $3,000 to study at the Iceland Academy of the Arts in Reykjavik. Kenney, a mathematics major from Richmond, Virginia, was awarded $4,500 to pursue studies in Hungary at the Budapest Semester in Mathematics. Hoy and Kenney are among nearly 1,000 American undergraduates from 386 colleges and universities across the United States selected to receive the prestigious award.

Two Bard College Students Win Prestigious Gilman Scholarships

Bard College students Kina Carney ’18 and Jessica Liu ’18 have both won highly competitive Benjamin A. Gilman International Scholarships to pursue studies abroad during the upcoming spring semester. Sponsored by the U.S. Department of State’s Bureau of Educational and Cultural Affairs, Gilman scholars receive up to $5,000 toward study abroad or internship costs.

Carney, a literature major, will take part in the Pitzer in Botswana program, which includes extended study trips in South Africa and Zimbabwe. Students live with host families, study local cultures, and work with scholars and experts in each country. Participants experience firsthand the concept and life of Ubuntu, the notion that defines the communal nature of the cultural values of the South African, Batswana, and Zimbabwean peoples. Ubuntu is indicated in the greetings that proclaim, “I am well if you are well,” and “my destiny is intricately intertwined with yours.”

Liu, a mathematics major, plans to pursue studies in the Budapest Semesters in Mathematics (BSM) program. Through BSM, mathematics and computer science majors study under the tutelage of eminent Hungarian scholar-teachers and receive the benefits of Hungary’s long tradition of excellence in mathematics education that includes combinatorics, number theory, and probability theory. BSM instructors are members of Eötvös University, the Mathematical Institute of the Hungarian Academy of Sciences, and Budapest University of Technology and Economics, the three institutions known for having educated more than half of Hungary’s highly acclaimed mathematicians. In keeping with Hungarian tradition, teachers closely monitor each student’s progress. Considerable time is devoted to problem solving and encouraging student creativity. Emphasis is on depth of understanding rather than on the quantity of material.

The Benjamin A. Gilman International Scholarship Program aims to diversify the students who study abroad and the countries and regions where they go. Rep. Gilman (R–N.Y.), who retired in 2002 after serving in the House of Representatives for 30 years and chairing the House Committee on International Relations, commented, “Study abroad is a special experience for every student who participates. Living and learning in a vastly different environment of another nation not only exposes our students to alternate views, but also adds an enriching social and cultural experience. It also provides our students with the opportunity to return home with a deeper understanding of their place in the world, encouraging them to be contributors rather than spectators in the international community.” During the spring 2017 application cycle, the program reviewed more than 2,700 applications for more than 850 awards.

Reem-Kayden Center Join our December graduating seniors in presenting their senior projects

Wednesday, December 31, 1969

Sunita Vatuk, City College of NY Hegeman 204 "It is notoriously hard to give a satisfactory answer to the question, 'What is mathematics?'" —Timothy Gowers

"One proposal, made in desperation, is 'What mathematicians do.'" —Ian Stewart

This women's art form is not part of academic research mathematics, and most of the experts in it are not formally educated, but the kolam-maker and the mathematician do share many patterns of thought. The range of mathematical connections found in kolams make it a particularly rich arena in which to explore that elusive definition of mathematics, by focusing on mathematical thinking outside of academia.

Dr. Vatuk has a PhD in differential geometry from Princeton University. As part of her teaching at University of Colorado (Boulder), Rutgers University (Piscataway), and City University of NY she has worked extensively with high school math teachers. That work sparked an interest in the existence and nature of mathematical thinking outside of research mathematics, including, but not limited to, origami and textile production. This talk is based on over 80 interviews with kolam experts and hundreds of designs she learned as a Fulbright scholar affiliated with the Institute of Mathematical Sciences, Chennai.

Wednesday, December 31, 1969

Kariane Calta, Vassar College Hegeman 204 In this talk, I will begin by describing how a question about the geodesic flow on translation surfaces led to an exploration of continued fraction algorithms associated to triangle groups. My aim is to describe how apparently different areas of mathematics can work together to give rise to interesting and sometimes surprising results.

Wednesday, December 31, 1969

Nicholas A. Scoville Ursinus College

Hegeman 204 Digital images surround us. They are found in our computers, iPhones, televisions, and more. Because they are so integrated into our lives, there is a constant need to manipulate and investigate these images. Anything that one might want to do with a digital image will inevitably involve some kind of mathematics, whether it be linear algebra, geometry, or topology. In this talk, we will introduce not only the topology of digital images, but topology in general. We'll discuss some of the main ideas in topology and use them to figure out what topology would mean in a digital setting. Our newfound knowledge of digital topology will then allow us to dene a digital version of the Hopf fibration, a function between spheres of different dimensions which links together circles in a beautiful and profound way. This talk will be accessible to undergraduates.

Wednesday, December 31, 1969

Heidi Burgiel, University of Massachusetts, Lowell Hegeman 204 Learn to fold a star-building unit -- a modification of the Sonobe module for unit origami. These modules combine to form right angled pyramids over equilateral triangles. Participants will have the opportunity to stellate a tetrahedron (creating a cube) and to explore the eight strictly convex deltahedra.

Wednesday, December 31, 1969

Hegeman 204 Sam Baumgartner Yuming Liu Andres Mejia Kirill Shakhnovskiy Yida Shao Darren Tirto Eric Zhang Lingxin Zhao

Wednesday, December 31, 1969

Ming-Wen An, Vassar College Hegeman 204 In the final stages of a long and costly drug discovery process, a drug compound is introduced into humans as part of a clinical trial. A clinical trial is a research study with a pre-defined protocol and is conducted in different phases. In oncology, as many as 60% of drug compounds that reach the last phase (Phase III) fail this final step. This high failure rate may reflect inappropriate evaluation of compounds in preceding Phase II trials, in which the primary endpoint is often binary tumor response, based on the Response Evaluation Criteria for Solid Tumors (RECIST). This motivates the search for alternative Phase II endpoints. In this talk, we will introduce clinical trials and survival analysis to contextualize the problem. Then we will describe our work evaluating alternative categorical and continuous tumor measurement-based endpoints for their ability to predict overall survival using data from real clinical trials.

Wednesday, December 31, 1969

Hegeman 204 Teagan DeCusatis Jessica Liu Rachel Nalecz Thuy Linh Nguygen Odett Salcedo Peter Servatius Kaylynn Tran Christian Yost

Wednesday, December 31, 1969

Hegeman 204 Eric Zhang, ’18 COMPACTNESS OF RIGID GRAPH Given a graph G, a framework is a straight line embedding of a G into d-dimensional space. Two frameworks of G are equivalent if the corresponding edges in the two frameworks have the same length. Given a collection of equivalent frameworks of G, a framework is compact if the distance between all pairs of vertices is minimal among the collection. We are mainly considering generic frameworks, in which the coordinates of the vertices of G are algebraically independent. In this paper, we studied compact frameworks in R and R^2.

Wednesday, December 31, 1969

Reem-Kayden Center

Wednesday, December 31, 1969

Hema Gopalakrishnan Sacred Heart University Hegeman 204 Recurrence relations arise in many fields of study. To solve a recurrence relation is to find an explicit formula for the numbers of the sequence generated by the recurrence. Informally, an ordinary generating function is a power series whose coefficients are the terms of a given sequence. In this talk, we will introduce the method of generating functions for solving linear recurrence relations with constant coefficients and apply this method to solve the Fibonacci recurrence relation.

Wednesday, December 31, 1969

Kerri-Ann Norton, Computer Science Program Hegeman 204 Breast tumor development is influenced by the individual properties of the tumor cells but also by other non-cancerous cells within its microenvironment. Based on experimental data, each tumor cell’s intrinsic properties are modeled, taking into account properties like cancer cell type and receptor numbers. In addition, we model the microenvironment’s influence on individual cancer cell properties, such as migration and proliferation. Then using agent-based modeling, we examine how individual cells interact with their microenvironment to form tumors and show how changes in that environment affect the tumor’s growth and invasion. From these results, we make predictions for potential therapies based on the interplay between the tumor and its microenvironment.

Wednesday, December 31, 1969

Moshe Cohen, Vassar College Hegeman 204 A line arrangement is a finite collection of lines in the plane. We can study this combinatorially by looking at intersections of lines. We can study this topologically by looking at the complement (in complex projective space). We can ask if the combinatorial information forecasts the topological information. When this does not occur, we obtain two different geometric arrangements; we call this a Zariski pair. There is no such pair of up to nine lines. Examples have been found with thirteen lines by Rybnikov in 1998 and with twelve lines by Guerville-Balle in 2014. Together with Amram, Sun, Teicher, Ye, and Zarkh, we investigate arrangements of ten lines. Together with an undergraduate student Liu last year, we investigate arrangements of eleven lines.

Wednesday, December 31, 1969

3rd floor Albee lounge Come and learn how you can help the Bard Math Circle provide access to mathematics enrichment throughout the Hudson River Valley. All Bard students are encouraged to attend and eat pizza, play puzzles and games, and find out more about the Bard Math Circle.

Wednesday, December 31, 1969

Albee 3rd floor lounge On behalf of the math faculty, I would like to welcome everyone back from what was hopefully a fun and relaxing summer break!

To celebrate your return, the math program will be having a get together this Monday 9/11 in the math common room from 5-6pm. There will be light refreshments and delightful conversion.

We would love if you could make it to hang out, talk, and reconnect. See you then!!

Wednesday, December 31, 1969

Antonios Kontos, Physics program Reem-Kayden Center Laszlo Z. Bito '60 Auditorium With three detections and counting, the Advanced LIGO gravitational-wave observatories have opened a new window into the Universe. For now, all the detected gravitational-waves originated from collisions of two black holes. The effect that these gravitational-waves have as they pass through space is to stretch and compress space-time, much like sound waves stretch and compress the air. To understand the challenge of detecting this effect here on Earth, imagine (if you can) that a reasonably strong gravitational wave changes the length of one kilometer by one thousandth of a proton's diameter. At this level of sensitivity, quantum mechanics and the Heisenberg uncertainty principle start playing a significant role and if we want to listen further into the Universe, we need to manipulate the quantum nature of light to our advantage. In this talk I will give an overview of gravitational waves, how LIGO detects them, and why quantum mechanics matters when measuring distances with such precision.

Wednesday, December 31, 1969

Reem-Kayden Center Join Science, Mathematics & Computer graduating seniors in presenting their senior projects.

Wednesday, December 31, 1969

Amir Barghi, Mathematics Program Hegeman 308 At a dinner party, each guest is assigned a seat along a long table, which seats 12 people. However, when all guests arrive, they decide to change things a little up by swapping seats. In order to minimize the amount of chaos, they have to follow the following three rules: a guest can keep their seat; two guests sitting next to each other or across the table can swap seats; three or more guests can swap seats in a cyclic fashion, provided that each person is moving one seat to the left or to the right or across the table. Assuming that all guests have showed up, how many possible seating rearrangements are there? Now consider the graph on the left. We want to place dominoes along some of the edges of this graph so that each vertex is covered by exactly one domino. We call any such placement of dominoes a domino tiling. How many domino tilings of this graph exits?

In this talk, we will explore the connection between these two problems by defining what the factorial of a graph is.

Prerequisites: A familiarity with graphs and counting arguments is a plus, but not required.

Wednesday, December 31, 1969

Maria Belk, Mathematics Program

Hegeman 308 In this talk, we investigate the important question of how many zombies are required to catch and eat a person in an enclosed structure. We model the structure with a graph, and we assume that the person can move much faster than the zombies. The minimum number of zombies required to catch an intelligent person is called the zombie number of the graph. This is a variation on the "cops and robbers" game from graph theory, which can be used to define the treewidth of a graph. We will discuss how the zombie number of a graph relates to the treewidth, and we will determine which graphs have zombie number 1 and 2. This talk will be accessible to anyone who is taking or has taken a 200-level mathematics course.

Wednesday, December 31, 1969

Lauren Rose, Mathematics Program Hegeman 308 Splines are piecewise polynomial functions that are often used to approximate complicated functions. They arise in various branches of applied mathematics, computer science and engineering. Applications include computer graphics and computer modeling, airplane design, and approximating solutions to partial differential equations. More recently, splines have been studied for their algebraic properties, and their defining equations have been generalized to arbitrary rings.

In this talk, I will describe Integer Splines on a graph, where both the edges and vertices of the graph are labeled with integers. The vertex labeling is called a spline if the difference between vertex labels is divisible by the corresponding edge label. I will report on recent work with Bard students, and open problems for the future.

Prerequisites: Familiarity with Linear Algebra and modular arithmetic is helpful, but not required.

Wednesday, December 31, 1969

Stefan Mendez-Diez Mathematics Program Hegeman 308 The purpose of this talk is to explore the interplay between mathematics and physics by taking a closer look at the theory of Electricity and Magnetism. We will start with the normal physicist's formulation of Maxwell's equations and then rewrite them from the perspective of a mathematician. This will allow us to describe what charge is as a mathematical object. We will then give a mathematical generalization of Maxwell's equations motivated by string theory and explore how physical phenomena can inform our understanding of the underlying mathematical structures. This talk should be accessible to anyone who has taken Math 213 or above.

Wednesday, December 31, 1969

Steve Simon, Mathematics Program Hegeman 308 Given any 3 shapes in R3 (e.g., a piece of ham, a hunk of cheese, and a slice of bread), does there exist a single plane that simultaneously cuts each shape into two pieces of equal volume? Can any shape in R2 be dissected into four pieces of equal area by some pair of perpendicular lines? By exploiting hidden geometric symmetries, we will show how equipartition problems such as these can be solved using powerful techniques from the seemingly unrelated eld known as algebraic topology. For instance, the positive answer to the rst problem above { the so-called Ham Sandwich" Theorem { ultimately reduces to a very deep result of Borsuk and Ulam: for any continuous map from a sphere to a plane, there must exist a pair of antipodal points on the sphere whose images coincide. While fairly advanced mathematics is not too far away, this talk requires only a familiarity with the intermediate value theorem to be understood. All are welcome to attend!

Wednesday, December 31, 1969

Japheth Wood, Mathematics Program

Hegeman 308 Come learn several historical methods to compute the area under a parabola, including approaches from Archimedes, Pascal, and Riemann. This talk is suitable for curious math students from Calculus I and beyond, and illustrates how creative approaches to problem solving can open up beautiful mathematical ideas.

Wednesday, December 31, 1969

Jim Belk, Mathematics Program Hegeman 308 A fractal is a geometric figure that exhibits a self-similar structure, meaning that the same patterns appear at a range of different scales. In this talk, I will explore the notion of symmetry in mathematics, and then describe some symmetries of fractal shapes that reflect their self-similar structure. The algebra of these symmetries can have certain unusual features, and I will discuss some surprising results that have been uncovered about this algebra as part of my research. This talk should be accessible to all math majors.

Refreshments to follow immediately in the Math Common Room.

Wednesday, December 31, 1969

Ethan Bloch Mathematics Program Hegeman 308 A very useful number associated with polyhedra is the Euler characteristic, which in the 2-dimensional case is V - E + F, where V, E and F are the number of vertices, edges and faces of a polyhedron, respectively. In this talk we consider the question of whether the Euler characteristic is locally determined, which means that it can be calculated as the sum of numbers determined in a neighborhood of each vertex of the polyhedron; there are combinatorial and geometric versions of this question, where the geometric version goes back to an idea of Descartes, from before Euler. We will then ask the analogous question regarding the Charney-Davis quantity of a polyhedron, which in the 2-dimensional case is 1 - (1/2)V + (1/4)E - (1/8)F. This talk should be suitable for all students who are currently in Math 261 (Proofs and Fundamentals) or beyond.

Refreshments to follow immediately in the Mathematics Common Room

Wednesday, December 31, 1969

John Cullinan, Mathematics Program Hegeman 308 In 1909 Arthur Wieferich proposed a way to attack Fermat's last theorem by introducing a variant on Fermat's little theorem. His idea has since been refined and now forms what is known as the "Wieferich Conjecture". Even though Fermat's last theorem has been proved, the Wieferich conjecture remains open and a major area of research in modern number theory. In this talk, I will explain the Wieferich conjecture, its modern geometric interpretation, and my current research project. This talk should be suitable for all students who are currently in Math 261 (Proofs and Fundamentals) or beyond. In particular, we will make extensive use of modular arithmetic.

Refreshments to follow immediately in the Math Common Room.

Wednesday, December 31, 1969

Zammy Diaz Columbia University Institute of Human Nutrition Campus Center Lobby Join Zammy Diaz, IHN Communications Center, to learn why the one-year MS Program in Nutrition Science may be a great gap or glide year for you.