Itamar Greenfield (Fall 2022)
Itamar Greenfield studied category theory over the 2022 fall. We used the text Category Theory in Context by Riehl, and covered the first half of the book. Topics covered included: characterizing equivalence of categories, the Yoneda lemma, limits and colimits. Itamar gave a blackboard talk to other DRP students towards the end of the project (recording).
Matthew Chen (Spring 2022)
Matthew Chen studied game theory over the 2022 spring. We used the text Game Theory by Fudenburg and Tirole, and covered most of parts I,II,III,IV. Some topics covered included: Nash equilibria, extensive-form games, repeated games, the purification theorem, mechanism design and the revelation principle.
Sherrie Tan (Summer 2021, Summer 2020)
Sherrie Tan studied algebraic topology over the 2021 summer. We used notes from Sarah Whitehouse's 2014-2015 algebraic topology course (archived link). Topics included homotopy, exact sequences, and simplicial and singular homology. Sherrie gave a blackboard talk to other DRP students at the end of the project where she proved Brouwer's fixed-point theorem using homology.
Sherrie Tan studied point set topology over the 2020 summer. We used the text Topology Without Tears by Morris and covered the majority of the book. Highlights include proving the fundamental theorem of algebra and visualizing some 3-manifolds. Sherrie gave a brief talk to other DRP students towards the end of the project (slides).
Brendan Polo (Spring 2021)
Brendan Polo studied elliptic curves during the spring. We used the text Elliptic Curves: Number Theory and Cryptography, 2nd edition by Washington, and covered the first four chapters of the book. Highlights included a proof of Pascal's Theorem using elliptic curves, as well as a proof of Hasse's theorem and applications to elliptic curves defined over finite fields.
Riley Guyett (Fall 2020)
Riley Guyett studied group theory during the fall. We used the text Abstract Algebra: Theory and Applications by Judson et. al, and covered the first half of the book. Highlights included UPC code validation, applications of group theory to elementary number theory (Euler's Theorem, Fermat's Little Theorem), and RSA Cryptography. Riley gave a brief talk to other DRP students at the end of the project about RSA (slides).