{"id":162,"date":"2016-01-01T07:57:22","date_gmt":"2016-01-01T15:57:22","guid":{"rendered":"https:\/\/math.berkeley.edu\/wp\/drp\/?page_id=162"},"modified":"2016-01-01T07:57:22","modified_gmt":"2016-01-01T15:57:22","slug":"past-drp-projects","status":"publish","type":"page","link":"https:\/\/wp.math.berkeley.edu\/drp\/past-drp-projects\/","title":{"rendered":"Past DRP Projects"},"content":{"rendered":"<h2>Past DRP Projects<\/h2>\n<p>This page contains a list of general topics for past DRP projects. If you&#8217;re looking for a project idea, it might be helpful to look through this list for inspiration. If you see any topics that sound cool but that you don&#8217;t know anything about, try Googling them to get more information. Wikipedia is also a valuable resource for general information about topics. Remember, you don&#8217;t need to have more than a general direction or topic for your project at the outset, and it&#8217;s totally fine if you don&#8217;t have any background in your topic.<\/p>\n<h3>Fall 2021<\/h3>\n<ul>\n<li>Partitions of Unity in Manifolds<\/li>\n<li>Model Theory and o-minimality<\/li>\n<li>Hyperbolic Geometry: Discovering a Strange New World<\/li>\n<li>Hash Functions, Bit Commitment, and Zero-Knowledge Proofs<\/li>\n<li>Numerical methods for solving PDEs<\/li>\n<li>Line bundles on elliptic curves<\/li>\n<li>Consistency of the continuum hypothesis with ZFC<\/li>\n<li>Proof of Kronecker-Weber Theorem for Quadratic Extensions<\/li>\n<li>Algebraic Combinatorics: Non-crossing partitions and Dyck paths<\/li>\n<\/ul>\n<h3>Spring 2017<\/h3>\n<ul>\n<li>Catalan Numbers<\/li>\n<li>Machine Learning<\/li>\n<li>Chip Firing<\/li>\n<li>Enriched Category Theory<\/li>\n<li>Quantum Computation<\/li>\n<li>Elementary Number Theory &#8211; Diophantine Equations<\/li>\n<li>Elliptic Curves<\/li>\n<li>Peano Space Filling Curve<\/li>\n<li>Filters and Ultrafilters<\/li>\n<li>The Word Problem for Coxeter Groups<\/li>\n<li>Vector Bundles and Projective Modules<\/li>\n<li>Information Theory<\/li>\n<li>Law of Quadratic Reciprocity<\/li>\n<li>Bootstrap Argument<\/li>\n<li>Markov Chains<\/li>\n<li>The Moduli Stack of Elliptic Curves<\/li>\n<li>Algebraic Topology<\/li>\n<li>The Classification of Semisimple Lie Algebras<\/li>\n<li>Factoring Sums of Squares in Z[i]<\/li>\n<\/ul>\n<h3>Fall 2016<\/h3>\n<ul>\n<li>Computation of the Class Number Formula<\/li>\n<li>Category Theory for the Sciences: Databases<\/li>\n<li>A Geometric Proof of the Quadratic Gauss Sum<\/li>\n<li>Gauss Winding Number<\/li>\n<li>Free Groups and Trees<\/li>\n<li>Brief Overview of Homology Theories<\/li>\n<li>Finite Difference Method for PDE and ODE<\/li>\n<li>Polynomial Hierarchy<\/li>\n<li>Homotopy Type Theory<\/li>\n<li>Representation Theory<\/li>\n<li>Integral extension and Convex Hull<\/li>\n<li>End Compactifications<\/li>\n<li>Universal Covering Space<\/li>\n<li>Weyl&#8217;s Equidistribution Theorem in Dynamical Systems<\/li>\n<li>The Uncertainty Principle<\/li>\n<li>On Hausdorff Gaps<\/li>\n<li>Algebraic Tools for Reverse Engineering Biological Systems<\/li>\n<li>Integral Closures and Nonsingular Plane Cuves<\/li>\n<\/ul>\n<h3>Spring 2015<\/h3>\n<ul>\n<li>Ax-Grothendieck Theorem: Basic Model Theory<\/li>\n<li>Algebraic Statistics in Biology<\/li>\n<li>Tensor &amp; Fluid Mechanics<\/li>\n<li>Morley Rank<\/li>\n<li>Elliptic Curve Digital Signature Algorithm<\/li>\n<li>Quadrature Schemes<\/li>\n<li>Dynkin Diagram<\/li>\n<li>Catenary Degree<\/li>\n<li>Riemann Mapping Theorem<\/li>\n<li>Galois Analysis of Fifth Degree Polynomials<\/li>\n<li>Hilbert&#8217;s Nullstellensatz<\/li>\n<li>Gauss\u2013Bonnet theorem<\/li>\n<li>Harmonic Analysis<\/li>\n<li>Hall&#8217;s Theorem<\/li>\n<li>Differential Forms<\/li>\n<li>Topics in Cryptography<\/li>\n<li>Counting Flags<\/li>\n<li>Demystifying the Fundamental Group with Category Theory<\/li>\n<li>Infinite Games and Determinacy<\/li>\n<li>Convolution inequalities<\/li>\n<\/ul>\n<h3>Fall 2015<\/h3>\n<ul>\n<li>Determinacy: Let&#8217;s Play a Game<\/li>\n<li>Dynkin diagrams<\/li>\n<li>The Kneser Graph<\/li>\n<li>Rational Points on Elliptic Curves<\/li>\n<li>Congruent Number Problem and Elliptic Curves<\/li>\n<li>Primes of form x^2 + ny^2 for infinitely many n<\/li>\n<li>Topologies<\/li>\n<li>Weierstrass Uniformization of Elliptic Curves<\/li>\n<li>Peter-Weyl Theorem<\/li>\n<li>Tate&#8217;s Thesis<\/li>\n<li>Geometric Classification of Semisimple Lie Algebras<\/li>\n<li>The Uniform Convergence of Fourier Series<\/li>\n<li>Dirichlet&#8217;s theorem on arithmetic progressions<\/li>\n<li>Elliptic curve cryptography<\/li>\n<li>Degree Structure of Turing Reducibility<\/li>\n<li>Self-adjoint operators and Observables in Quantum Mechanics<\/li>\n<li>A Continuous but Nowhere Differentiable Function<\/li>\n<li>Maxwell&#8217;s Equations on Manifolds<\/li>\n<li>A Basic Result on Maps of Riemann Surfaces<\/li>\n<li>Differential Forms and Stokes Theorem<\/li>\n<li>A quick proof of Leray-Hirsch via hypercohomology<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Past DRP Projects This page contains a list of general topics for past DRP projects. If you&#8217;re looking for a project idea, it might be helpful to look through this list for inspiration. If you see any topics that sound cool but that you don&#8217;t know anything about, try Googling them to get more information. &hellip;<\/p>\n","protected":false},"author":81,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-162","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/drp\/wp-json\/wp\/v2\/pages\/162","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/drp\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/drp\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/drp\/wp-json\/wp\/v2\/users\/81"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/drp\/wp-json\/wp\/v2\/comments?post=162"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/drp\/wp-json\/wp\/v2\/pages\/162\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/drp\/wp-json\/wp\/v2\/media?parent=162"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}