14 citations · 33 across the 9 of their papers we have counts for
10 papers
Natural Cohomology on
Pablo Solis
A vector bundle on a projective variety has a natural cohomology if for every twist its cohomology is concentrated in a single degree. Eisenbud and Schreyer conjectured there shoul…
Hunting Vector Bundles on
Pablo Solis
Boij-Söderberg theory concerns resolutions of graded modules over a polynomial ring over a field. Specifically Boij-Söderberg theory gives a description of the cone of Betti diagra…
Infinite type toric varieties and Voronoi Tilings
Pablo Solis
An infinite type toric variety is a normal toric variety given by a fan with infinitely many cones. We construct examples in this paper coming from representation theory of loop gr…
Nodal Uniformization of G-bundles
Pablo Solis
We give a survey of uniformization results for principal bundles on curves. We provide a proof of uniformization for nodal curves; this result is a special case of work of Belkale…
Stable gauged maps
E. González, P. Solis, C. Woodward
We give an introduction to moduli stacks of gauged maps satisfying a stability conditition introduced by Mundet and Schmitt, and the associated integrals giving rise to gauged Grom…
Properness for scaled gauged maps
E. González, P. Solis, C. Woodward
We give an algebraic proof of properness of moduli stacks of gauged maps satisfying a stability conditition introduced by Mundet and Schmitt. The proof combines a git construction…
A complete degeneration of the moduli of -bundles on a curve
Pablo Solis
For a semi simple group G it is known the moduli stack of principal G-bundles over a fixed nodal curve is not complete. Finding a completion requires compactifying the group G. How…
A Wonderful Embedding of the Loop Group
Pablo Solis
Index of notation added. Shortening of some section, simplification of some of the arguments, some small added results and strengthening of thm 3.10. Also a significant re-writing…
A proof of the Kauffman-Harary Conjecture
Thomas W. Mattman, Pablo Solis
We prove the Kauffman-Harary Conjecture, posed in 1999: given a reduced, alternating diagram D of a knot with prime determinant p, every non-trivial Fox p-coloring of D will assign…
On the Harary-Kauffman Conjecture and Turk's Head Knots
Nicholas E. Dowdall, Thomas W. Mattman, Kevin Meek +1
The m,n Turk's Head Knot, THK(m,n), is an "alternating (m,n) torus knot." We prove the Harary-Kauffman conjecture for all THK(m,n) except for the case where m \geq 5 is odd and n \…