Parth Sarin Curriculum Vitae September 2017 Email: parthsarin@tamu.edu Website: http://www.parthsarin.com/ LinkedIn: http://linkedin.com/in/parth-sarin Current and Past Positions Spring 2017 Undergraduate Researcher, Texas A&M University, College Station Pursuing research in quantum information theory. The goal is to understand tensor networks (also called Matrix Product States [MPS] or Projected Entangled Pair States [PEPS]), and specifically when certain flattenings of the tensor network state become injective. This is a mathematical restatement of a set of problems related to quantum max flow, and quantum information theory more broadly. 2014 2017 Research Assistant, Texas A&M University, College Station Designing and writing maplets to change the pedagogical process by which Calculus is often taught. Database and algorithm design to surround the maplet architecture Research Interests Representation theory of finite spaces and Lie algebras Tensors o Tensor geometry o Tensor networks and wiring diagrams o Complexity of matrix multiplication Algebraic topology o Topology towards complexity theory (mostly via covering space theory related to input and output algorithmic spaces, see, e.g., Smale [1987, On the topology of algorithms, I]) o Cohomology theory o Simplicial manifolds Academic Training Summer 2015 AY 2015-16 Fall 2015 Spring 2016 AY 2016-17 Fall 2016 Spring 2017 Calculus II (MATH 152), Texas A&M University, College Station AP Chemistry, A&M Consolidated HS, College Station Mechanics (PHYS 218), Texas A&M University, College Station Several Variable Calculus (MATH 221), Texas A&M University, College Station Optics and Electromagnetism (PHYS 208), Texas A&M University, College Station Honors Linear Algebra (MATH 323), Texas A&M University, College Station AP United States History, A&M Consolidated HS, College Station AP English Language and Composition, A&M Consolidated HS, College Station Differential Equations (MATH 308), Texas A&M University, College Station Honors Advanced Calculus I (MATH 409), Texas A&M University, College Station Honors Linear Algebra II (MATH 423), Texas A&M University, College Station Directed Studies, Texas A&M University, College Station Topics covered: o Multilinear algebra (tensors, tensor spaces, decompositions of V #, irreducible GL(V) modules in V (, wiring diagrams)
Curriculum Vitae: Parth Sarin 2 o Representation theory (Schur s lemma, the group algebra of S (, representations of S ( in V (, general decomposition of V ( as S ( and GL(V) modules Schur- Weyl duality, Kronecker coefficients and characters of S (, the Littlewood- Richardson rule, the Pieri formula, weights and weight spaces, Lie algebras) o Algebraic geometry (projective space, several projective varieties, secant varieties, Segre varieties, Veronese varieties, Grassmannians) Summer 2017 The University of Chicago Mathematics REU (Apprentice), University of Chicago, Chicago, IL Advisor: Dr. Peter May (https://math.uchicago.edu/~may/) Topics covered: Probability, Algebraic topology, Geometry Paper on Algebraic topology towards complexity theory (involving cup length of subset of cohomology ring and studying the braid group) and dynamics towards approximating polynomial roots AY 2017-18 AP Government, A&M Consolidated HS, College Station AP Microeconomics, A&M Consolidated HS, College Station AP English Literature, A&M Consolidated HS, College Station AP Art History, A&M Consolidated HS, College Station Fall 2017 Honors Modern Algebra I (MATH 415), Texas A&M University, College Station Honors Principles of Analysis I (MATH 446), Texas A&M University, College Station Research (MATH 491), Texas A&M University, College Station Research statement: Study tensor networks (also called Matrix Product States [MPS] or Projected Entangled Pair States [PEPS]) to understand when certain flattenings of the tensor network state become injective. This is a mathematical restatement of a set of problems related to quantum max flow, and quantum information theory more broadly. TAMU GPA: 4.0 [Fall 2017 not included] AMCHS GPA: 4.0 [Unweighted, as of April 2017] Funding and Research 2017 Pursuing research under Dr. JM. Landsberg in the geometry of tensor networks 2014 2017 MyMathApps: NSF DUE CCLI / TUES Grant 0737209 / 1123255 (Awarded to Dr. Philip B. Yasskin) Honors and Awards July 2017 Summer 2017 Spring 2017 March 2, 2017 Awarded the Pi Mu Epsilon Student Speaker Award for a distinguished presentation at MAA Mathfest 2017. Talk (see below): From phylogenetics to statistical physics: tensor wiring diagrams and the applications of tensors to the sciences Accepted into and participated in the apprentice REU at the University of Chicago Led by Professor J. Peter May (http://math.uchicago.edu/~may/) Inducted into the Texas A&M Chapter of ΠΜΕ (Pi Mu Epsilon) ΠΜΕ is the U.S. honorary national mathematics society for undergraduate students Due to academic standing and accomplishments, Texas A&M inducted me as a high school student Inducted into the A&M Consolidated High School Chapter of NHS (National Honor Society) From the NHS website: NHS serves to recognize those students who have demonstrated excellence in the areas of scholarship, service, leadership, and character
Curriculum Vitae: Parth Sarin 3 Fall 2016 Summer 2016 March 2015 January 2015 Summer 2013 Summer 2011 Selected for the Physics 218 (Mechanics) Peer Leader Program based on performance and application Goal of the program is to replace traditional TA-led recitation sections with peer groups consisting of ~8 undergraduate students and a peer leader Graduated from the Summer Mathematics and Research Training camp at Texas A&M University Focus on number theory and combinatorics Competed in the Texas A&M Math Department Integral Bee Solved problems involving integration under a time limit Won 1 st place in the High School division Ranked top 3 in the Undergraduate Division Competed for Texas A&M University at the JMM in San Antonio in the Math Wrangle Wrote proofs to math problems in 30 minutes and presented them Won 2 nd place in the tournament Graduated from the Complex Circle camp at Texas A&M University Graduated from SEE-Math camp at Texas A&M University Service and Outreach April 2017 Summer 2016 April 2016 Summer 2014 Summer 2013 Volunteer for the TAMU Math Fair Helped children solve problems about finding Hamiltonian paths and the expected duration of a random walk along various graphs Helped TAMU Math Faculty lecture to middle school students on a wide variety of math topics Helped students create animations using the Maple computer algebra system Volunteer for the TAMU Math Fair Helped students solve the Two Eggs Problem o For reference, see the abstract on p. 191 from J. Wood and P. Yasskin: http://www.maa.org/sites/default/files/pdf/mathfest/mf15-abstracts.pdf Goal is to increase public understanding of and appreciation for mathematics, specifically among middle school students Honors in Speech and Debate June 2017 March 2017 December 2016 October 2016 2016-17 Academic Year June 2016 Qualified for the National Speech and Debate Association s National Tournament in Birmingham, Alabama in Senate Debate Qualified for and attended the Texas Forensics Association s State Tournament in Original Oratory Quarterfinalist in Public Forum Debate at the University of Texas Longhorn Classic (Finalists received bids for the Tournament of Champions) Octofinalist in Public Forum Debate at the Bellaire High School Debate Tournament (Quarterfinalists received bids for the Tournament of Champions) Chosen as Captain of Public Forum Debate at A&M Consolidated High School Qualified for and attended the National Speech and Debate Association s National Tournament in Salt Lake City, Utah in Public Forum Debate
Curriculum Vitae: Parth Sarin 4 March 2016 January 2016 Qualified for and attended the Texas Forensics Association s State Tournament in Public Forum Debate Quarterfinalist in Public Forum Debate at the Churchill Classic (Finalists received bids for the Tournament of Champions) Selected Presentations and Publications The Cup Length in Cohomology: A Bound on Topological Complexity. REU at the University of Chicago. The University of Chicago, IL. August 2017. o Abstract: Polynomial solving algorithms are essential to applied mathematics and the sciences. As such, reduction of their complexity has become an incredibly important field of research. We present a topological approach to constructing a lower bound for the complexity of a polynomialsolving algorithm, and give a concrete algorithm to do this in the case that deg f = 2, 3, 4. o Link to publication: https://math.uchicago.edu/~may/reu2017/reupapers/sarin.pdf From phylogenetics to statistical physics: tensor wiring diagrams and the applications of tensors to the sciences. MAA MathFest. Mathematical Association of America. Chicago, IL. July 2017. o Abstract: Due to their usefulness in organizing data, tensors are used in almost every scientific discipline. Applications aside, tensors also give rise to beautiful geometric structures. To understand them, mathematicians use wiring diagrams. Dating back (at least) to Clifford in 1881, these diagrams provide a powerful realization of many complex tensors, aiding in our understanding of their structure, applications, and geometry. We ll discuss tensor wiring diagrams and the application of tensors to phylogenetics and/or algebraic statistics, time permitting. o Link to publication: http://resume.parthsarin.com/files/mathfest-2017-tensor-talk.pdf The Dissemination of Gossip. MAA MathFest. Mathematical Association of America. Chicago, IL. July 2017. o Abstract: We will discuss a Math Circle on the dissemination of gossip. Each student in a group of n students (perhaps 4,5 or 6) has a different pet. Everyone wants to know who has which pet. They communicate by gossiping. Initially each student only knows their own pet. When two students gossip, they exchange all the information they have with one another. In a group of n students, what is the minimum number of conversations it takes until everyone knows everything? This activity is based on the Gossip Protocol for computing as discussed at https://en.wikipedia.org/wiki/gossip_protocol o Link to publication: http://resume.parthsarin.com/files/mathfest-2017-gossip-talk.pptx Other Presentations and Publications Intro to Carothers Real Analysis. Math 409. Texas A&M University, TX. Fall 2016 How fast can you gossip?. TAMU Math Circle. Texas A&M University, TX. November 5, 2016. Rating Website for the Maplets for Calculus. 96 th Annual Meeting of the Texas Section of the MAA. Stephen F. Austin University, TX. April 1, 2016. Skills Audio editing o Host of the podcast, Life, Puberty, and the Pursuit of Happiness Public speaking o Member of A&M Consolidated Speech and Debate team for 3 years (see: Honors in Speech and Debate) o Chosen as a peer leader, to teach Mechanics to undergraduates in recitation sections
Curriculum Vitae: Parth Sarin 5 Piano: o Distinguished National Guild Member for performances in 2010-2014 o Two Superior Distinctions by the Brazos Valley Music Teachers Association for Solo Festival performances (2008-2011, 2012-2015) o Five Gold Distinctions by the Brazos Valley Music Teachers Association for knowledge of music theory (2 perfect scores; 5 gold medals overall) Computer languages: Proficient in Java, C++, Matlab, Python, Ruby, LaTeX Spoken languages: o Proficient in English (native language) o Limited working proficiency in Spanish and Hindi Organizations National Honor Society Member since 2017 Pi Mu Epsilon (ΠΜΕ) Member since 2017 National Speech and Debate Association Member since 2014 Miscellaneous Citizenship: USA Place of Birth: Bryan, TX Birthday: May 8, 2000