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Columbia Summer Undergraduate Math Research Program in Paris

Language of Instruction: English
Location:
Paris,
France
Term: Summer

Engage in mathematical research under the guidance of faculty members and graduate students from both Paris and New York in a small group setting with students from Paris. 

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The Departments of Mathematics at Columbia University and Université Denis Diderot are pleased to offer a joint Summer Undergraduate Research Experience in Paris. With an equal number of students from each institution, this six and a half week program will allow you explore the experience of doing mathematical research in a small group of 12 peers.

Program Overview

  • Offered as a Summer Undergraduate Research opportunity through the math department
  • Conduct intensive mathematical research with peers from French institutions guided by faculty from both France and Columbia in a small group environment
  • Benefit from exposure to a different approach to mathematics with students and faculty from one of the largest mathematical research institutes in Europe
  • Live with other program participants in a residence in the heart of Paris

Eligibility and Application

  • Must be a currently enrolled student at Barnard College, Columbia College, Columbia Engineering, or the School of General Studies
  • Rising junior or rising senior Math majors preferred
  • All students must meet the basic requirements for studying abroad: a 3.0 cumulative GPA and good academic and disciplinary standing in their home school
  • Although knowledge of French is not required, some study of the language may be useful for students living in Paris

Academics

The course is oriented around a research question. The first sessions will be devoted to providing the background needed for the research and the subsequent time will be spent engaged in daily group research.

Project Title: Toric Varieties

Abstract: In algebraic geometry, the term "toric variety" refers to an algebraic variety containing an algebraic torus, on which the canonical action of the torus on itself extends. Toric varieties form a rich class of algebraic varieties which can be described in a combinatorial way and which are also closely related to convex geometry. In modern Diophantine analysis, toric varieties are also used to give geometric interpretations of classic Diophantine problems.

The purpose of this project is to study toric varieties from various points of view, as well as modern research topics according to the taste of the participants such as: proof of inequalities of convex geometry via the Hodge index theorem, Okounkov bodies, heights on toric varieties etc.

Life in Paris

Housing

All Columbia students will live in double rooms at the Maison des Mines et des Ponts.

Meals

Meals are not included and there is no meal plan. However, there are grocery stores, boulangeries, fromageries, and charcuteries where students can buy food for casual dining.

There are several low-budget travel guides that give information about where to eat in Paris, as well as many blogs devoted to eating in Paris. We recommend taking the time to do some research beforehand if you are unsure about what to expect.

Activities

Throughout the program, there will be complementary activities that will help you to explore the life and culture of Paris, as well as mathematically relevant points of interest.

Daily Living and Schedule

The program will take place at both the Columbia Global Center in Paris and Paris VII and some commuting will be required depending on the day. While there will be adequate time for exploration of the city, the research will be intensive and for several hours per day.

Location

Columbia Global Centers|Paris at Reid Hall is the home base of the program and where you will spend half of your time. Reid Hall is a small group of buildings owned and administered by Columbia. It serves as a base for other Columbia programs during the summer including Columbia Summer Core in Paris: Art Humanities and Music Humanities and Columbia Summer in Paris and as an educational center for other American universities and for scholars from around the world. For over a century, its long and distinguished past of intellectual, artistic, and cultural exchange has made it significant to the relationship between France and the United States.

Located in the lively Montparnasse (sixth) district of Paris, near the Luxembourg Gardens and within walking distance of the Latin Quarter and several branches of the University of Paris, Reid Hall was constructed in the early 18th century, before the French Revolution. Modern additions have enlarged the facility, creating an interior courtyard and private garden. Reid Hall primarily houses administrative offices and classrooms and also has a small reference library, a reading room, lounges, a multimedia lab, and two large conference rooms. Students have access to WiFi in all common areas of Reid Hall.

Paris VII: Université Denis Diderot Paris is a multi-disciplinary research university founded in 1970, known for its distinguished teaching in the sciences, particularly in mathematics. The mathematics department at Paris VII is a founding member of several research networks, notably the Institut de Mathématiques de Jussieu-Paris Rive Gauche (IMJ-PRG), which is the largest mathematical research institute in Europe. Members of the Paris VII faculty represent every major branch of mathematics and include two Fields Medal winners.

People

Staff

The faculty and program are supported by the staff of the Columbia Undergraduate Programs in Paris. While you may encounter any number of staff members onsite, you will mostly interact with the Columbia Undergraduate Programs director, Séverine Martin-Hartenstein and Cathy Collins.

Columbia Faculty

Michael Harris, Program Director

Michael Woodbury, Undergraduate Research Director

Paris VII Faculty

Financial Considerations

Because this program does not offer academic credits, there are no tuition or housing changes. All local transportation and program activities are included.

Cost breakdown coming soon.

Resources for Accepted Students

Fact Sheet

Advisers:
Discipline:
STEM
Eligibility:
Barnard College, Columbia College, Columbia Engineering, Columbia General Studies
Language of Instruction:
Location:
Paris,
France
Region:
Europe
Term:
Summer

Dates & Deadlines

Summer
2019
Application Deadline: 
Friday, March 8, 2019
Admissions Decision Date: 
Friday, March 15, 2019
Program Dates: 
Monday, June 10, 2019 to Thursday, July 25, 2019