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Saturday, June 08, 2019

Mathematicians help train the next generation of positive thinkers | Science & Technology - Penn: Office of University Communications

A trio of researchers paves the way for future progress in an up-and-coming field that unites geometry and number theory in powerful new ways, according to Erica K. Brockmeier, Science News Officer.

Karemaker, Hartmann, and Bell all know the importance of summer math programs and supportive mentors as inspiration for their own career paths. “It’s a really good opportunity to meet a whole lot of new people who are all extremely friendly and supportive, and I think that atmosphere is something that we’re definitely aspiring to,” Karemaker says about the upcoming conference. 
Photo: Penn: Office of University Communications

As postdocs across the region embark on summer research projects and internships, Penn mathematicians Renee Bell, Julia Hartmann, and Valentijn Karemaker are using their time between semesters to address challenges in a mathematics field called arithmetic geometry, and to help early-career researchers gain skills important to their success as the next generation of mathematicians. 

Unlike fields like biology or engineering, where an aspiring academic fresh off of earning a Ph.D. joins a lab, mathematicians must establish their research agendas quicker and more independently. “Postdocs do have a faculty mentor formally, but they are usually not part of a bigger project,” says Hartmann. 

To assist these peridoctoral researchers—those currently working on a Ph.D. or who have recently graduated—the Penn trio, with Padmavathi Srinivasan from Georgia Tech and Isabel Vogt from MIT, organized a summer conference. Participants will focus on problems in arithmetic geometry, a relatively young field that applies techniques from algebraic geometry to solve problems in number theory. 

Seemingly simple questions in number theory such as “Can the sum of two cubes be a cube?” are, in reality, very difficult to prove mathematically. One example is Fermat’s Last Theorem, a number theory problem solved using techniques from geometry more than 350 years after its proposal...

“[Arithmetic geometry] is a field that’s not very old yet, less than a century old, when compared to some other branches of mathematics, like number theory which is thousands of years old. There are more and more people, especially young people, who are now working on this intersection, and that’s something we all appreciated and recognized,” says Karemaker. 

Researchers at the conference will also learn key skills for their careers like writing mathematical research papers, establishing a research agenda, managing large collaborations, and writing grant applications. Senior advisors and mentors will be on hand to talk to discuss their own technical challenges and math problems, as well as to provide general career guidance. 
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Source: Penn: Office of University Communication