This page contains the notes from the UMN Combinatorics and Algebra REU 2022.

Problem 1: Minimal Matchings of dP3 Cluster Variables

Mentor: Gregg Musiker

TA: Carolyn Stephen, Sylvester Zhang

• Lecture

• TA Section

• Paper Presentation

  • Aztec Castles

• Final Presentation

Problem 2: q_Analogue of Random Shuffling

Mentor: Sarah Brauner

TA: Patty Commins

• Lecture

• TA Section

• Paper Presentation

  • Dieker, Saliola, "Spectral analysis of random-to-random Markov chain", Theorem 5, Ben Przybocki

  • Dieker, Saliola, "Spectral analysis of random-to-random Markov chain", Theorem 38, Ilani Axelrod-Freed

• Final Presentation

Problem 3: Polarizations of Strongly Stable Ideals

Mentor: Ayah Almousa

TA: John O'Brien

• Lecture

• TA Section

• Final Presentation

Problem 4: Classifying Divides of Finite Mutation Type

Mentor: Pasha Pylyavskyy

TA: Sylvester Zhang

• Lecture

• TA Section

• Final Presentation

Problem 5: Refined Enumeration of Core Partitions

Mentor: Hannah Burson

TA: Robbie Angarone

• Lecture

• Paper Presentation

  • Bijective proof of the number of (s,s+2)-core partitions with distinct parts, Veronica Lang

• Final Presentation

Problem 6: Column-Strict Tableaux and Cactus Group

Mentor: Vic Reiner

TA: Anh Hoang

• Lecture

• Paper Presentation

  • Promotion and Evacuation, Janabel Xia

  • Growth Diagram for Dual Evacuation, Ryan Lynch

• Final Presentation

Problem 7: Measuring the Space of Whittaker Functions

Mentor: Claire Frechette

TA: Carolyn Stephen

• Lecture

Problem 8: Cohen-Macaulayness of ASM Varieties

Mentor: Patricia Klein

TA: John O'Brien

• Lecture

• Final Presentation