## Wednesday, October 24, 2017

### David Cox, Amherst College

### Tangents to Four Unit Spheres

Abstract: How many lines can be tangent to four spheres of radius one sitting in three-dimensional space? I will use this question to introduce enumerative algebraic geometry. The lecture will include an introduction to projective space, Bezout's Theorem, and mirror symmetry from mathematical physics. Parts of the lecture will use some ideas from multivariable calculus.

4:30 pm in Seeley Mudd 206. Refreshments in Seeley Mudd 208 at 4.

## Friday, November 10, 2017

### Rachel Ward, University of Texas at Austin

### Mathematics for k-means clustering and beyond

Amherst College Mathematics and Statistics Connecticut Valley Colloquium (CVC) talk for 2017-18.

Abstract: Under the hood of any modern algorithm for "big data" analysis is a step where the data is clustered into a smaller number of groups. The most widely-used clustering objective is the k-means algorithm, which aims to partition a set of n points into k clusters in such a way that each observation belongs to the cluster with the nearest mean, and such that the sum of squared distances from each point to its nearest mean is minimal. In general, this is a hard optimization problem, requiring an exhaustive search over all possible partitions of the data into k clusters in order to find the optimal clustering. At the same time, fast heuristic algorithms are often applied in many data processing applications, despite having few guarantees on the clusters they produce. In this talk, we will introduce new algorithms and techniques for solving the k-means optimization problem, based on semidefinite relaxation, and present geometric conditions on a set of data such that the algorithm is guaranteed to find the optimal k-means clustering for the data. The new algorithm has surprising connections to matrix factorization and manifold learning, and we conclude by discussing several open problems.

4:30 pm in Seeley Mudd 206. Refreshments in Seeley Mudd 208 at 4:00 pm. The talk will be followed by a dinner at 30 Boltwood Restaurant. Reservations are REQUIRED and cost $20 per person. Email awtorrey@amherst.edu for a reservation.

## Statistics Professor Nick Horton Honored for his Contributions to the Statistics Community

Prof Nick Horton is the 2017 recipient of the annual Lagakos Distinguished Alumni Award, given by the Department of Biostatistics at Harvard University. The citation of the award describes his impactful leadership and service to the profession, his distinguished contributions to statistical methodology and computing, and his commitments to teaching and statistical education.

Nick also recently received the prestigious Founders Award, presented at the 2017 Joint Statistical Meetings (JSM) in Baltimore. The other three awardees are Wendy Martinez, Director of the Mathematical Statistics Center, Bureau of Labor Statistics; Jane Pendergast, Professor, Department of Biostatistics and Bioinformatics, Duke University School of Medicine; and John Eltinge, Assistant Director for Research & Methodology, U.S. Census Bureau. The citation read, “The ASA is extremely pleased to present our highest honor to Wendy, Jane, Nick, and John. They have dedicated their careers to the field of statistics and demonstrated impressively high standards that have helped strengthen the experiences of colleagues throughout the association’s membership and beyond. From teaching future generations of critical thinkers the theories and applications that can lead to new scientific discoveries, to calculating and analyzing government data in robust, meaningful and accurate ways, to advancing research that will lead to more effective healthcare, they each have left a tremendous footprint in the scientific discipline that is statistics,” said ASA President Barry Nussbaum.

## Mu Sigma Rho award plus new group of inductees

Ningyue (Christina) Wang '16 has been chosen as the recipient of the 2016 Boston Chapter of the American Statistical Association Mu Sigma Rho Award. This annual award recognizes one outstanding statistics undergraduate per year in the BCASA region (Rhode Island, Massachusetts, Maine, New Hampshire, and Vermont). Mu Sigma Rho is the national statistics honor society. Christina was selected as the inaugural winner of the award based on her outstanding achievements in statistics (she had been inducted into Mu Sigma Rho in 2015).

In addition to Christina's award, eleven Amherst College students were inducted into Mu Sigma Rho. Congratulations to Jonathan Che, Stephany Flores-Ramos, Paul Gramieri, Connor Haley, Azka Javaid, Rishi Kowalski, Levi Lee, Amanda Rosenbaum, Muling Si, Sarah Teichman, and Alex Titelbaum for their academic achievements and distinction.

**Amherst Students win Best in Show and Best in Group at Five College ASA DataFest **

Congratulations to Jonathan Che, Pei Gong, Timothy Lee, Shelly Tang, and Sarah Teichman for being named "Best in Group" and "Best in Show" at the Five College ASA DataFest. Other winners from Amherst included the team consisting of Jordan Browning, Jerry Chen, Brendan Seto, Leonard Yoon, and Jingwen Zhang. DataFest is a data analysis competition where teams of up to five students have a weekend to attack a large, complex, and surprise dataset. More than 130 undergraduate students from the Five Colleges participated in this year's event. More details can be found at http://www.science.smith.edu/datafest/2016/04/04/recap-of-winners-from-datafest-2016/

### Mathematics Professor Michael Ching named Lazerowitz Lecturer (April 14, 2016)

Congratulations to Michael Ching, who has been named as the 2015-2016 Lazerowitz Lecturer. His talk, entitled "Shape" took place on Thursday, April 14th in Paino Lecture Hall (Beneski). The abstract states that the universe around us is full of fascinating shapes: we see them in the natural world, we put them in our buildings, we see them in the remnants of exploded stars. Einstein proposed that the universe itself has an interesting shape - that space is curved. In the world of our imagination, there are even more fantastic shapes that have beautiful and interesting properties: worlds that you can walk all the way around and come back as a mirror image of yourself, surfaces that can be knotted like higher-dimensional pieces of string.

In this talk he will describe how mathematicians think of shapes and understand their fundamental properties. How can we tell two shapes apart? What ways can two different shapes be similar? How can we “measure” shape? Can we hope to build a catalog of all possible shapes?

This ethereal topic has recently started to have more down-to-earth applications. The emergence of “big data” has led to a need for new ways to analyze that data, and one such analysis is to look for interesting shapes therein. Where before we might be happy to find that a set of data forms a straight line, now there are ways to detect circles, surfaces and higher-dimensional shapes hidden in the numbers. These higher-order patterns can illuminate unexpected relationships and tell you something that traditional data analysis might miss.

### Cox, Little, and O'Shea to Receive 2016 AMS Steele Prize for Exposition

The AMS Leroy P. Steele Prize for Exposition was awarded to three mathematicians: **David Cox** (Amherst College), **John Little** (College of the Holy Cross), and **Donal O'Shea** (New College of Florida) "for their book *Ideals, Varieties, and Algorithms*, which has made algebraic geometry and computational commutative algebra accessible not just to mathematicians but to students and researchers in many fields."

Algebraic geometry has a reputation for being impenetrably technical and abstract. By requiring only linear algebra as a prerequisite, the book by Cox, Little, and O'Shea invites a broad audience of readers into this central branch of mathematics. Using geometry to introduce core topics and appealing to computational theory to prove fundamental results, they complement the development of theoretical results with applications to such topics as automated theorem proving and robotics. All of this is delivered with crystal-clear exposition and top-quality writing.

"Even more impressive than [the book's] clarity of exposition is the impact it has had on mathematics," the prize citation states. "*CLO*, as it is fondly known, has not only introduced many to algebraic geometry, it has actually broadened how the subject could be taught and who could use it." The book helped bring the topic of computational algebra into the mathematical mainstream. In particular, the book's presentation of the theory of Gröbner bases "has done more than any other book to popularize this topic." Gröbner bases provide a way to efficiently automate certain calculations in algebraic geometry. The subject of Gröbner bases has boomed in recent years, in part because of significant applications to such diverse problems as oil exploration, software design, genetics, and robot kinematics.

Originally published by Springer Verlag in 1992, the fourth edition of *CLO* appeared just this year. The book has truly become a classic. It not only has provided many of today's mathematicians with their first grounding in algebraic geometry, but also has brought this area of mathematics to the service of scientists and engineers. All three authors are top-flight mathematicians at small colleges; O'Shea was at Mount Holyoke College for more than 30 years before becoming the president of New College of Florida in 2012. Their book shows how small colleges make signal contributions to the advancement of mathematics, the training of future mathematicians, and the applications of mathematics to other disciplines. The AMS Steele Prize is one of the highest distinctions in mathematics.

Cox received the Lester R. Ford Prize from the Mathematical Association of America (2012) and was elected as a Fellow of AMS (2013). Little has received distinctions for his outstanding service to the College of the Holy Cross, including its Distinguished Teaching Award (2003) and the Anthony and Renee Marlon Professorship in the Sciences (2012-2015). In 2008, O'Shea received the Peano Prize for his book *The Poincaré Conjecture: In Search of the Shape of the Universe* (Walker & Company, 2006).

#### Ongoing - Math and Stats Table every Monday, noon - 1:30, Valentine Terrace Room A MOST weeks

Past News and Events can be found in the Archive.

### DataFest Results

Amherst College was represented by 4 teams (a total of 18 students) at the Five College DataFest held the weekend of March 27-29, part of a national competition sponsored by the American Statistical Association. This was the second year for the event in the Five Colleges. Participants spent 25 hours over the course of the weekend tackling a large dataset, and gave 6-minute presentations summarizing their insights. 6 teams out of 16 total were awarded prizes. Amherst teams won awards for: Best Business Value (Team: Jo-Jo ToAlTrev), Best Pitch (Team: 95% Confident), and Best Use of External Data (Team: The Women in Black). We were thrilled by the turn-out and hard work from Amherst students, and look forward to participation next year. Congratulations to all participants!

- Best Pitch: 95% Confident (Amherst College): Paul Gramieri, Caleb Ki, Levi Lee, Thomas Matthew, and Albert Yu
- Best Business Value: Jo-Jo ToAlTrev (Amherst College): Johannes Ferstad, Jon Jordan, Thomas Savage, Trevor Smith, Alexander Titelbaum
- Best Use of External Data: Women in Black (Amherst College): Muling Si, Jenny Xiao, Qi Xie, Jingwen Zhang

View a calendar of events in the Five College area.