Dheeran E. Wiggins

Phone: +1 (630) 835 3436
Email: dheeran2@illinois.edu
Pronunciation: Dheeran (dee-rin) Eugene (yu-jeen) Wiggins (wig-ins)
Curriculum Vitae

I am a third-year mathematics undergraduate at the University of Illinois studying algebra, topology, and quantum information. Recently, monoidal categories (e.g., \(\textsf{Hilb}, \textsf{Mod}_R, \textsf{Rel}\)) and categorical quantum theory have my attention.

During the summer of 2025, I became a MathQuantum Fellow at the University of Maryland, College Park. In August, I was at the Summer School on Geometry, hosted by the Utrecht Geometry Centre at Universiteit Utrecht.

Notes

• Math 595: Representation-theoretic Methods in QIT (Felix Leditzky; in progress)
  distance measures, Werner states
• Math 595: Topological Field Theories in 2D (James Pascaleff; in progress)
  Atiyah-Segal axioms, 1D TQFT classification, Frobenius algebras
• Math 526: Algebraic Topology II (Jeremiah Heller; in progress)
  singular cohomology, universal coefficients, (co)limits, \(\lim^1\), Milnor exact sequence
• Pontryagin-Thom Construction (Gijs Heuts, Miguel Barata)
  regular values, framed submanifolds, homotopy groups \(\pi_n X \), stabilization, cobordisms, Hopf fibration, cobordism groups \(\Omega_k^{\mathrm{f}}\), Pontryagin-Thom
• Matrix Lie Groups (Douwe Hoekstra, Sven Holtrop)
  matrix exponentials and logarithms, matrix lie groups, Lie algebras, Baker-Campbell-Hausdorff, Lie subgroups, Lie subalgebras, Lie's Third Theorem
• Math 527: Homotopy Theory (Charles Rezk; in progress)
  nerves, \(\infty\)-categories, fibrations, anodyne, slices, Joyal lifting, \(\mathsf{Cat}_{\infty}\), \(\pi_n : \mathsf{Kan}_* \to \mathsf{Set}_*\), presentability, stability, spectra, operads
• Math 525: Algebraic Topology I (James Pascaleff; in progress)
  homotopy, \(\pi_1(X,x_0)\), covering spaces, lifting, CW complexes, \(\Delta\)-complexes, Galois covers, singular and cellular homology, Eilenberg-Steenrod axioms
• An Introduction to Sheaf Cohomology
  abelian categories, (pre)sheaves, functor categories, derived functors, sheaf cohomology, Čech cohomology, first cousin problem
• MATH 501: Abstract Algebra II (Igor Mineyev)
  categories, (co)limits, \(\operatorname{Hom}\) and \(\otimes_R\), adjunctions, (co)homology, \(\operatorname{Tor}_n^R\) and \(\operatorname{Ext}^n_R\), spectral sequences, multilinear algebra, representations
• MATH 500: Abstract Algebra I (Charles Rezk)
  free groups, \(\textsf{Grp}\), actions, \(\textsf{Set}_G\), group rings, domains, \(\textsf{Mod}_R\), coproducts, semisimple rings, modules over PIDs, fields, Galois correspondence
• MATH 535: General Topology (Igor Mineyev)
  homeomorphisms, invariants, \(\ell^p(\mathbb{N}, \mathbb{R})\), separability, embeddings, \(Y^X\), \(\mathcal{B}(X,Y) \), \(\mathcal{C}(X,Y)\), completions, \(\pi_1: \mathsf{Top}_{*} \to \mathsf{Grp}\)
• ECE 498: Quantum Information Processing Theory (Eric Chitambar)
  state spaces, tensor products, \(\operatorname{SU}(2) \simeq \operatorname{SO}(3)\), CPTP channels, Pauli twirling, POVMs, LOCC, teleportation, nonlocality
• MATH 418: Intro to Abstract Algebra II (Andy Hardt)
  domains, \(R[x]\) irreducibility, fields and towers, \(\operatorname{Gal}(\mathbb{K}/\mathbb{L})\), \(\mathbb{C}\mathrm{P}^n\), projective and affine Nullstellensatz
• MATH 424: Honors Real Analysis (Eugene Lerman)
  topology, metric spaces, differentiation, integration, interchange of limit operations, Lebesgue measure and integration, \(L^1(E,d \mu)\)

Talks

• Apr 2025 A model for the infinite tensor product of groups: Insights from quantum information at the Illinois Undergraduate Research Symposium. Talk advised by Igor Mineyev.
• Mar 2025 On noncommutative graphs and Poulin's stabilizer formalism at the Rose-Hulman Undergraduate Mathematics Conference. Talk advised by Roy Araiza.
• May 2024 Winter Spaces and the Stabilizer Formalism at the Illinois Mathematics Lab Open House with Anderson et al. Poster advised by Roy Araiza.
• Apr 2024 Modeling a Viral Epidemic With a Concurrent ''Misinfodemic'' at the Research Institute Spring Scientific Research Poster Reception. Poster advised by Anthony Solomonides.
• Apr 2024 Modeling a Viral Epidemic With a Concurrent ''Misinfodemic'' at the Illinois Undergraduate Research Symposium. Talk advised by Anthony Solomonides.
• Apr 2024 Winter Spaces and the Stabilizer Formalism at the Illinois Quantum Information Science & Technology (IQUIST) World Quantum Day with Anderson et al. Poster advised by Roy Araiza.
• Apr 2023 Identification and estimated yield of background events in a search for doubly charged Higgs bosons at CMS at the American Physical Society April Meeting with Anne et al. Poster advised by Peter Dong.
• Apr 2023 Identification of optimal production channels for dark photon searches at the American Physical Society April Meeting with Anne et al. Poster advised by Peter Dong.
• Apr 2023 Unidirectional build architecture: Refactoring a HEP data collection codebase at the Annual IMSAloquium. Talk advised by Peter Dong.
• Apr 2022 An investigation of triboson decays into four-lepton final states at the Annual IMSAloquium with George Bayliss and Jesus Fileto. Talk advised by Peter Dong.

Lately

• Coffee: Most mornings I use the Fellow Ode Gen 2 with a classic ceramic V60. At the moment, I am drinking Counter Culture Finca El Puente.
• Self-study: I am slowly working through
  • Tensor Categories by Dmitri Nikshych, Pavel Etingof, and Shlomo Gelak.
  • Handbook of Categorical Algebra 2: Categories and Structures by Francis Borceux.
  • Categories for Quantum Theory: An Introduction by Jamie Vicary and Chris Heunen.
  • Theory of Operator Algebras I by Masamichi Takesaki.
  • Models and Ultraproducts: An Introduction by J. L. Bell and A. B. Slomson.
• Reading: When I have time, I pick up A History of Western Philosophy by Bertrand Russell. I regret not spending more of my daylight in a book, though. I recently finished The Stranger by Albert Camus, and I am now reading Stoner by John Williams and The Trial by Franz Kafka.
• Plants: Besides my collection of mostly hydroponic pothos, I have been tending to a new money tree and a lucky "bamboo."