{"id":957,"date":"2025-12-15T15:20:35","date_gmt":"2025-12-15T23:20:35","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/drp\/?p=957"},"modified":"2026-01-14T12:37:21","modified_gmt":"2026-01-14T20:37:21","slug":"fall-2025-wrap-up","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/drp\/2025\/12\/15\/fall-2025-wrap-up\/","title":{"rendered":"Fall 2025 Wrap-Up"},"content":{"rendered":"\n

With 76 pairings, this was another banner semester for the DRP. We are, as always, grateful for the effort of the mentors and department staff who make all this possible. We couldn’t do it without them.<\/p>\n\n\n\n

Now for one of my favorite parts of the program: sharing the completed projects! The pairs who submitted a final paper or do a presentation at our end-of-semester conference are featured below. We hope you find their work entertaining and educational — and that it might serve as a resource if you’re considering starting a DRP project yourself.<\/p>\n\n\n\n

Mentee<\/th>Mentor<\/th>Project<\/th><\/tr><\/thead>
Ariana Abel<\/td>Akash Narayanan<\/td>Connectedness vs Path Connectedness<\/td><\/tr>
Nicholas Ballesteros<\/td>Alexander Burka<\/td>Stone Duality for Boolean Algebras and Cylindric Algebras<\/a><\/td><\/tr>
Edward Beckon<\/td>Leonard Tomczak<\/td>Dirichlet’s Theorem on Arithmetic Progressions<\/td><\/tr>
Ryan Chan<\/td>Zoe McDonald<\/td>The It\u00f4 Integral<\/a><\/td><\/tr>
Juan Claver<\/td>Yahya Bashandy<\/td>Local Kronecker-Weber<\/a><\/td><\/tr>
Antonio Cortijo<\/td>Liza Jacoby<\/td>Descriptive Set Theory<\/td><\/tr>
Amelia Craciun<\/td>Marco David<\/td>Enumerative Geometry<\/td><\/tr>
Omkar Guha<\/td>Jake Hofgard<\/td>Combinatorial Upper Bounds for Self-Avoiding Walks on the Integer Lattice<\/a><\/td><\/tr>
Michelle Holland<\/td>Alexander Burka<\/td>Lindstr\u00f6m’s Theorem<\/td><\/tr>
Yang Hu<\/td>CJ Dowd<\/td>p<\/mi>p<\/annotation><\/semantics><\/math>-Adic Hodge Theory<\/a><\/td><\/tr>
Diana Hu<\/td>Ruslans Aleksejevs<\/td>Arnold\u2019s Topological Proof of Abel\u2019s Impossibility Theorem<\/a><\/td><\/tr>
Michael Lan<\/td>Katalin Berlow<\/td>Nielsen\u2013Schreier theorem<\/a><\/td><\/tr>
Dylan Lu<\/td>John Nolan<\/td>B\u00e9zout\u2019s Theorem in Algebraic Geometry<\/a><\/td><\/tr>
Runze Lu<\/td>Lewis Pan<\/td>Markov Chain Monte Carlo<\/a><\/td><\/tr>
Shijie Lyu<\/td>Ely Sandine<\/td>Navier-Stokes Equations for 2-Dimensional Incompressible Slightly Viscous Flow Along Curved Wall<\/a><\/td><\/tr>
Benedikt Vilji Magn\u00fasson<\/td>Lizzie Pratt<\/td>A Geometric Introduction to Representation Theory<\/td><\/tr>
Nathan Mann<\/td>Smita Rajan<\/td>Algebraic Geometry<\/a><\/td><\/tr>
Dron Mongia<\/td>Thomas Browning<\/td>Real Analysis with Filters<\/a><\/td><\/tr>
Connor Murray<\/td>Jerry Yang<\/td>De Rham Cohomology<\/td><\/tr>
Andrew Nguyen<\/td>Nilay Patel<\/td>Why Are All Meteorologists Eventually Wrong?<\/a><\/td><\/tr>
Vignesh Nydhruva<\/td>Akash Narayanan<\/td>Algebraic Number Theory<\/a><\/td><\/tr>
Partha Krishna<\/td>Swapnil Garg<\/td>Verma Modules and the Harish-Chandra Isomorphism<\/a><\/td><\/tr>
Yifei Qi<\/td>Joao Basso<\/td>On Matrix Analysis Methods in Quantum Entropy<\/a><\/td><\/tr>
Xiang Shi<\/td>Vinh-Kha Le<\/td>The Application of Machine Learning and Deep Reinforcement Learning on Quantum Optimization<\/a><\/td><\/tr>
Ailsa Sun<\/td>Etienne Phillips<\/td>Yoneda’s Lemma<\/a><\/td><\/tr>
Yuxin Tan<\/td>Sai Sanjeev Balakrishnan<\/td>Primes of the form x<\/mi>2<\/mn><\/msup>+<\/mo>n<\/mi>y<\/mi>2<\/mn><\/msup><\/mrow>x^2+ny^2<\/annotation><\/semantics><\/math><\/a><\/td><\/tr>
Sofia Torelli<\/td>Izzy Detherage<\/td>Cheeger’s Inequality<\/a><\/td><\/tr>
Ayisha Umar<\/td>August No\u00eb<\/td>A Nonstandard Proof of the Bolzano-Weierstrass Theorem<\/td><\/tr>
Ethan Eugene Wynner<\/td>Will Fisher<\/td>Some Notions in \u00c9tale Cohomology<\/a><\/td><\/tr>
Stephanie Yao<\/td>Alex Feiner<\/td>Elliptic Curves and Finding Torsion Points<\/td><\/tr>
Brian Zhou and Woong Choi<\/td>Reed Jacobs<\/td>Fundamental Groups<\/a><\/td><\/tr><\/tbody><\/table><\/figure>\n","protected":false},"excerpt":{"rendered":"

With 76 pairings, this was another banner semester for the DRP. We are, as always, grateful for the effort of the mentors and department staff who make all this possible. We couldn’t do it without them. Now for one of my favorite parts of the program: sharing the completed projects! The pairs who submitted a …<\/p>\n","protected":false},"author":83,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-957","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/drp\/wp-json\/wp\/v2\/posts\/957","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/drp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/drp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/drp\/wp-json\/wp\/v2\/users\/83"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/drp\/wp-json\/wp\/v2\/comments?post=957"}],"version-history":[{"count":3,"href":"https:\/\/wp.math.berkeley.edu\/drp\/wp-json\/wp\/v2\/posts\/957\/revisions"}],"predecessor-version":[{"id":999,"href":"https:\/\/wp.math.berkeley.edu\/drp\/wp-json\/wp\/v2\/posts\/957\/revisions\/999"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/drp\/wp-json\/wp\/v2\/media?parent=957"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/drp\/wp-json\/wp\/v2\/categories?post=957"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/drp\/wp-json\/wp\/v2\/tags?post=957"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}