2020. 2. 10. 11:28ㆍ카테고리 없음
Including number theory, algebraic geometry, and combinatorics We have large groups of researchers active in number theory and algebraic geometry, as well as many individuals who work in other areas of algebra: groups, noncommutative rings, Lie algebras and Lie super-algebras, representation theory, combinatorics, game theory, and coding. A number of members of the algebra group belong to the, which runs activities and supports grad students and postdocs in its areas of interest. Undergraduate upper division courses (and honors version, ).
Oct 17, 2014 - Abstract Algebra Research Topics for Undergraduates”. Which you may undertake as capstone projects or undergraduate honors theses.
Linear algebra. (and honors version, ). Introduction to abstract algebra. Second course in abstract algebra. (Instructor's choice; usually Galois Theory). Introduction to number theory.
Elementary algebraic geometry. The Mathematics Department also offers, at the undergraduate level, courses which may include algebraic topics along with others: Problem Solving (H90), Experimental Courses (191), a Special Topics course (195), and several courses of directed and independent individual and group work (196-199). Graduate courses. General theory of algebraic structures.
Algebraic combinatorics. Groups, rings and fields. Multilinear algebra and further topics. Ring theory. Representation theory.
Homological algebra. Number theory. Algebraic curves. Algebraic geometry. Group theory.
Seminar -, David Eisenbud. Seminar - Number theory, Kenneth Ribet Spring 2009.
Topics in Algebra - Tropical geometry, Bernd Sturmfels. Topics in Algebra - Infinitesimal geometry, Mariusz Wodzicki Fall 2008. Seminar - Algebraic geometry, David Eisenbud and Daniel Erman. Seminar - Discrete mathematics, Bernd Sturmfels. Seminar - Representation theory, geometry and combinatorics, Mark Haiman and Nicolai Reshetikhin. Seminar - Student arithmetic geometry seminar, Martin Olsson Student Seminar. Student algebraic and arithmetic geometry seminar, David Brown, Daniel Erman and Anthony Varilly 2007-2008.
Hot Topics - Derived algebraic geometry and topology, Peter Teichner. Seminar - David Eisenbud. Seminar - Representation theory, geometry and combinatorics, Mark Haiman and Nicolai Reshetikhin Spring 2008. Topics in Algebra - Robert Coleman Fall 2007. Topics in Algebra - Locally finite lie algebras and their representations with a view toward open problems, Ivan Penkov. Seminar - Student representation theory, geometry and combinatorics, Vera Serganova and Peter Tingley. Seminar - Number theory, Kenneth Ribet.
Seminar - Perverse sheaves, Joel Kamnitzer and Xinwen Zhu. Name Title Research Interests Visiting Scholar Algebraic combinatorics, discrete homotopy and homology theory Visiting Miller Professor Combinatorics Lecturer Number theory, Galois representation Visiting Scholar Character theory of finite groups; applications of group theory to biology; combinatorics Lecturer Hopf algebras and their finite dimensional representations Lecturer Number theory and combinatorics Lecturer Number theory, p-adic automorphic forms Visiting Scholar Hopf algebras, quantum groups Lecturer Algebraic combinatorics. Name Title Research Interests Professor Symplectic topology and mirror symmetry Professor Emeritus Combinatorial game theory, Algebraic coding theory, Electrical engineering, Computer science Professor Numerical analysis, matrix theory, algebra and combinatorics, computational complexity Professor Emeritus General algebra, Logic Professor Emeritus Representations and actions of topological groups, Operator algebras Professor Non-commutative harmonic analysis, Operator algebras, Quantum geometry Professor Model theory and applications to number theory.
Below you will find a listing of mathematical papers. See for archived versions of recent honors theses. Senior Honors Theses/Graduation with Distinction Papers directed by mathematics faculty members 2010-present. Lindsey Brown An Application of Abstract Algebra to the Neural Code for Sound Localization in Barn Owls (2016) with M. Reed.
David Builes The Large Cardinal Hierarchy (2016) with R. Hodel. Kyle Casey Siegel Modular Forms (2016) with L. Saper.
Bryan Runjing Liu Modeling the Effects of Positive and Negative Feedback in Kidney Blood Flow Control (2016) with A. Layton. Francois Thelot A Maximum Entropy Based Approach for the Descriptino of the Conformational Ensemble of Calmodulin from Paramagnetic NMR (2016) with M.
Maggioni and B. Daniels. Will Victor Efficient algorithms for Traffic Data Analysis (2016)computer science with P. Agarwal.
Paul Ziquan Yang Morphisms with Only Mild Singular Fibers and Bertini Theorems over Finite Fields (2016) with C. Schoen. Rex Zhitao Ying Approximation Algorithms of Dynamic Time Warping and Edit Distance (2016) computer science with P. Agarwal. Roger Zou Deformable Graph Model for Trackng Epithelial Cell Sheets in Florescence Microscopy (2016)computer science with C. Tomasi.
Anne Talkington Modeling the Dynamics of Cancerous Cells in vivo (2015) with R. Durrett. Rowena Gan Geometry of Impressionist Music (2015) with E.
Miller. David Hemminger Augmentation Rank of Satellites with Braid Pattern (2015) with L. Cornwell. Mandy Jiang Dynamic random network model for human papilloma virus transmission (2015) with M. Ryser. Hunter Nisonoff Efficient Partition Function Estimatation in Computational Protein Design (2015) with M. Maggioni.
Eugene Rabinovich The Conformal Manifold in N=(2,2) SCFTs (2015)physics with R. Plesser. Marshall Ratliff Introducing the Cover tree to Music Information Retrieval (2015) with P. Bendich. Brett Schnobrich Heisenberg-Weyl Group, Subspace Packings, and Image Processing (2015) with R. Calderbank.
Christy Vaughn Stochastic Study of Gerrymandering (2015) with J. Mattingly. Aashiq Dheeraj A Stochastic Spatial Model for Tumor Growth (2014) with R. DurretT.
Joshua Izzard Rank p^2 Representations of Semisimple Lie Algebras (2014) with J. Getz. Kathleen Lan Coalescing random walks on n-block Markov chains (2014) with K. McGoff. Leslie Lei Lei Infinite Swapping Simulated Tempering (2014) with J. Lu.
Julia Ni A convex approach to tree-based wavelet compression (2014) with A. Thompson. Jiarou Ivy Shen Merge times and hitting times of time-inhomogeneous Markov chains (2014) with D.
Sivakoff. Daniel Stern Low-Order Lagrangians Depending on a Metric and a Matter Field of Arbitrary Rank (2014) with H. Bray.
Daniel Vitek Knot Contact Homology and the Augmentation Polynomial (2014) with C. Cornwell. Alexander Wertheim Complex Multiplication on Elliptic Curves (2014) with L. Saper. Luxi Wei Modeling Credit Risk using Rating and Environmental Factors (2014) with R. Durrett. Timothy Chang On the existence of a simple winning strategy in the T(4.3) knot game (2013) with D.
Herzog. Conrad de Peuter Modeling basketball games as alternating renewal-reward processes and predicting match outcomes (2013) with R. Durrett. Bryan Jacobson A practical approximation of persistent local homology (2013) with P.
Bendich. Kara Karpman Simulating mucociliary transport using the method of regularized Stokelets (2013) with A. Layton. Carmen Lopez Modeling the folate pathway in Escherichia coli (2013) with A.
Layton. James Malleree Strategy and honesty based comparison of preferential ballot voting methods (2013) with H. Bray. William Zhang Evolutionary dynamics in host pathogen model (2013) with R. Durrett. Ben Bellis Investigation of a Local Computation of the Signature from the Triangulation of a Manifold (2012) with M. Stern.
Adrian Chan Pricing financial derivatives with multi-task machine learning and mixed effects method (2012) with J. Bouvrie. Kyu Won Choi Relative contributions of common jumps in realized correlations (2012) with A.
Thesis On Abstract Algebra Groups Pdf
Petters. Veronica Ciocanel Analysis of the nonlinear dynamics of the forced planar string pendulum (2012) with T. Witelski.
Kaveh Danesh A branching process model of ovarian cancer (2012) with R. Durrett. Theo Frehlinghuysen Carbon sequestration via forest management techniques (2012) with D. Kraines. Yingyi Shen A study of edge toric ideals using associated graphs (2012) with S.
Mapes. Daniel Thielman Complex-balanced steady state of chemical reaction networks that contain an Eulerian cycle (2012) with C. Berkesch.
Kaitlin Daniels Noise driven Transitions between stable equilibria in stochastic dynamical systems (2011) with A. Athreya. Alan Guo Lattice point methods for combinatorial games (2011) with E. Miller. Nils Hultgren Centrality and network analysis: A perturbative approach to dynamical importance (2011) with I.
Matic. Hans Kist Estimating carbon sequestration potential in the boreal forests (2011) with D. Kraines.
Misha Lavrov Invariants in Legendrian links in the solid torus (2011) with D. Rutherford. Philip Pham Tubuloglomerular feedback signal transduction in the loops of Henle (2011) with A. Layton.
Thames Sae Sue A simple cardiac model exhibiting stationary discordant alternans (2011) with D. Schaeffer.
Max Tabachnik An analysis of preferential ballot voting methods (2011) with H. Bray. Bo Waggoner A model of the foot and ankle in running (2011) with E. Bouzarth.
Wutichai Chongchitmate Classification of Legendrian knots and links (2010) with L. Ng. Jason D. Lee Multiscale analysis of dynamic graphs (2010) with M.
Maggioni. Jeremy Semko Statistical analysis simulations of coarsening droplets coating a hydrophobic surface (2010) with T. Witelski. Amy Wen Model of feedback-mediated dynamics of coupled nephrons with compliant thick ascending limbs (2010) with A. Layton 2000-2009. Jason Ferguson Factorization of Primes in Biquadratic Extensions of Q (2009) with C. Schoen.
Jared Haftel A Closer Look at ADC multivariate GARCH (2009) with M. Huber. Mark Hallen Improving accuracy and scope of quantitative FRAP analysis (2009) with A. Layton. Andy Ng Retinoid Transport in the Vision cycle (2009) with J. Mercer. Aaron Pollack Relations between special derivations arising from modular forms (2009) with R.
Hain. Jesse Thorner Simplicial homology and DeRham's theorem (2009) with W.
Allard. Barry Wright III Objective measures of preferential ballot voting systems (2009) with H. Bray. Michael Bauer Existence and stability of patterns arising from square wave forcing of the damped Mathieu equation (2008) with A. Catlla. Tirasan Khandhawit On Legandrean and transverse knots (2008) with L.
Ng. Aalok Shah An overview of fast marching and optimal control methods for trajectory optimization (2008) with W. Allard. Charles Staats III Application of discrete geometry to the construction of Laurent-rational zeros (2008) with S. Sharif. Elliott Wolf Computational pathways to Godel's first incompletness theorem (2008) with R. Hodel.
Lingen Zhang The motion of sets of vortices (2008) with T. Witelski. Morgan Brown An algorithm for tracking persistence pairing of a discrete homotopy of Morse functions on S^2 (2007) with J.Harer.
Thesis On Abstract Algebra Examples
Brandon Levin Class field theory and the problem of representing primes by binary quadratic forms (2007) with L. Saper. Stepan Paul Lines and conics relative to degenerating divisors in CP^2 (2007) with J. Davis. James Zou 3-D reconstruction and topological analysis of root architecture (2007) with J. Harer.
Pradeep Baliga Dynamic cellular automata model of toll plaza traffic flows (2006) with W. Mitchener. Adam Chandler Dynamic cellular automata model of toll plaza traffic flows (2006) with W. Mitchener. Matthew Fischer Mapping model of cardiac-membrane dynamics (2006) with D.
Schaeffer. Qinzheng Tian Simulation of Newtonian fluid flow between rotating cylinders (2006) with T. Witelski. Yee Lok Wong Models of instant runoff voting (2006) with J. Mattingly. Oaz Nir Mechanical Arms and Algebraic Topology (2005) with J.Harer. Mayank Varia Explict calculaton of the L invariant for Kummer surfaces (2005) with J.
Hanke. David Arthur On the higher Hasse-Witt matrices and related in variants (2004) with W. Pardon. Suzy Borgschulte A mathematical approach to the panting of dogs (2004) with M. Reed.
Lauren M. Childs Scaling population dynamics from the macroscopic to the microscopic (2004) with T. Kepler. Ryan Letchworth Wavelet methods for numerical solutions of differential equations (2004) with S. Roudenko.
David Marks Coadjoint orbits and geometric quantization (2004) with M.R. Plesser. Lori Peacock Distributions of the small eigenvalues of Wishart matrices (2004) with B. Rider. Lindsay C. Piechnik Smooth reflexive 4-polytopes have quadratic triangulations (2004) with C.
Haase. Matthew Toups A solution to the D0-D4 system of equations (2004) with M. Stern.
Jenna VanLiere Mathematically modelling the growth and diversification of T-cell populations (2004) with T. Kepler. Matthew J. Atwood Evaluating singular and nearly singular integrals numerically (20(2003) with J.T. Beale.
Marie Guerraty Controlling alternans in a cardiac map model (2003) with M. Romeo. Meredith C. Houlton Classification of critical curves and preliminary analysis of caustics (2003) with A. Petters. Steven R.
Nicklas Envy and satisfaction in the public goods game (2003) with D. Kraines. Dane R. Voris A numerical approach to the Mt/Mt/Nt queue with abandonment (2003) with B. Rider.
Melanie Wood Invariants and relations of the action of the absolute Galois group on dessins d'enfants and the algebraic fundamental group of the punctured sphere (2003) with R. Hain. Thomas W.
Thesis Abstract Format
Finley Efficient Myrinet routing (2002) with W. Allard. Samuel W. Malone Alternative Price Processes for Black-Scholes: Empirical Evidence and Theory (2002) with A. Petters.
Carl Miller Exponential Iterated Integrals and the Solvable Completion of Fundamental Groups (2001) with R. Hain. Daniel Neill Optimality under Noise: Higher Memory Strategies for the Alternating Prisoner's Dilemma (2001) Computer Science with D. Kraines. Luis Von Ahn Models of the language of set theory and Zermelo Frankel axioms (2000) with R.
Hodel 1999 and earlier. Christopher Beasley Superconformal theories from Branes at Singularities (1999) Physics with R.
Plesser. Alexander Brodie Measurable Cardinals (1999) with R. Hodel. Jeffrey DiLisi The Biology and Mathematics of the Hypothalamic-Pituitary-Testicular Axis (1999) with M. Reed. Garrett Mitchener Lattices and Sphere Packing (1999) with R.
Hain. Andrew O.
Dittmer Generalized Formulas for Circular Polygons (1998) with R. Hain. Richard R.
Schneck Set Theory and Cardinal Arithmetic (1997) with R. Hodel. Tung T. Tran Counting Independent Subsets in Nearly Regular Graphs (1997) with G. Lawler. Paul A.
Dreyer Knot theory and the human pretzel game (1995) with J. Harer. Paul J. Koss Effects of noise on the iterated prisoner's dilemma (1995) with D. Kraines. Jeff Vanderkam Eigenfunctions of an acoustic system (1994) with T.
Beale. Linie Chang Mathematics and immunology: Modeling antigen and antibody interactions (1993) with M. Reed. Sang H. Chin Action of the Torelli group on the 3-fold cover of G-hole torus (1993) with R. Hain.
Jennifer Slimowitz Transitions of gaps between the integers N satisfying Nq.