My research explores the interplay between algebra and combinatorics. I specialize in combinatorial representation theory, which observes that we can gain insights into abstract mathematical structures by realizing them in more concrete ways. In recent years, I have become especially involved in an emerging area known as super-representation theory, a theory that uses a precise form of fudging to better understand problems that are known to be mathematically impossible. This new interest has also inspired me to study combinatorial Hopf algebras in more detail.

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Topics of interest: Representation theory, character theory, supercharacter theory, groups of Lie type, Hecke algebras, symmetric functions, Hopf algebras and monoids

MATH 6900 - Independent Study
Instructor consent required for undergraduates. May be repeated up to 6 total credit hours. (Spring 2019 UC Boulder)

MATH 6940 - Master's Candidate for Degree
This course is for students preparing for the no-thesis option for a master's degree. The content is set by the students' advisors. (Spring 2019 UC Boulder)

MATH 8900 - Independent Study
Instructor consent required for undergraduates. May be repeated up to 6 total credit hours. (Spring 2019 UC Boulder)

MATH 8990 - Doctoral Dissertation
All doctoral students must register for not fewer than 30 hours of dissertation credit as part of the requirements for the degree. For a detailed discussion of doctoral dissertation credit, refer to the Graduate School portion of the catalog. (Spring 2019 UC Boulder)

MATH 2001 - Introduction to Discrete Mathematics
Introduces the ideas of rigor and proof through an examination of basic set theory, existential and universal quantifiers, elementary counting, discrete probability, and additional topics. Department enforced prerequisite: MATH 1300 or MATH 1310 or APPM 1345 or APPM 1350 (minimum grade C-). (Fall 2018 UC Boulder)

MATH 6130 - Algebra 1
Studies group theory and ring theory. Department enforced prerequisite: MATH 3140. Instructor consent required for undergraduates. (Fall 2018 UC Boulder)

MATH 6900 - Independent Study
Instructor consent required for undergraduates. May be repeated up to 6 total credit hours. (Fall 2018 UC Boulder)

MATH 6940 - Master's Candidate for Degree
This course is for students preparing for the no-thesis option for a master's degree. The content is set by the students' advisors. (Fall 2018 UC Boulder)

MATH 8900 - Independent Study
Instructor consent required for undergraduates. May be repeated up to 6 total credit hours. (Fall 2018 UC Boulder)

MATH 8990 - Doctoral Dissertation
All doctoral students must register for not fewer than 30 hours of dissertation credit as part of the requirements for the degree. For a detailed discussion of doctoral dissertation credit, refer to the Graduate School portion of the catalog. (Fall 2018 UC Boulder)

MATH 8990 - Doctoral Dissertation
All doctoral students must register for not fewer than 30 hours of dissertation credit as part of the requirements for the degree. For a detailed discussion of doctoral dissertation credit, refer to the Graduate School portion of the catalog. (Summer 2018 UC Boulder)

MATH 6900 - Independent Study
Instructor consent required for undergraduates. May be repeated up to 6 total credit hours. (Spring 2018 UC Boulder)

MATH 6940 - Master's Candidate for Degree
This course is for students preparing for the no-thesis option for a master's degree. The content is set by the students' advisors. (Spring 2018 UC Boulder)

MATH 8900 - Independent Study
Instructor consent required for undergraduates. May be repeated up to 6 total credit hours. (Spring 2018 UC Boulder)

MATH 8990 - Doctoral Dissertation
All doctoral students must register for not fewer than 30 hours of dissertation credit as part of the requirements for the degree. For a detailed discussion of doctoral dissertation credit, refer to the Graduate School portion of the catalog. (Spring 2018 UC Boulder)