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  1. Erik Carlsson . Email: ecarlsson at math dot ucdavis dot edu Office: MSB 2101. Phone: 530-754-0274. I am a Full Professor in the Mathematics department at the University of California, Davis.

  2. Erik L Carlsson. Representation theory, algebraic geometry, combinatorics. Office: MSB 2101. Phone: 530-754-0274. Email: ecarlsson@math.ucdavis.edu. Roger Casals. Contact and Symplectic Topology. Office: MSB 3214. Email: casals@math.ucdavis.edu. Courses: MAT 67. Office Hours: M 2-3pm; W 2-3pm. Rishidev Chaudhuri. Neural Computation and Neuroscience

  3. Aug 25, 2015 · Erik Carlsson, Anton Mellit. We present a proof of the compositional shuffle conjecture, which generalizes the famous shuffle conjecture for the character of the diagonal coinvariant algebra. We first formulate the combinatorial side of the conjecture in terms of certain operators on a graded vector space V∗ whose degree zero part is the ring ...

  4. A new construction for sublevel set persistence. Erik Carlsson, John Carlsson. June 16, 2021. Abstract. We construct a filtered simplicial complex (XL, fL) associated to a subset X ⊂ Rd, a function f : X → R with compactly supported sub-level sets, and a collection of landmark points L ⊂ Rd.

  5. Oct 1, 2023 · Erik Carlsson, John Carlsson. The alpha complex is a fundamental data structure from computational geometry, which encodes the topological type of a union of balls B(x; r) ⊂ Rm for x ∈ S, including a weighted version that allows for varying radii. It consists of the collection of "simplices" σ = {x0,...,xk} ⊂ S, which correspond to ...

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