Summer Research at New Paltz (2026)

• This summer program is supported by NSF LEAPS-MPS (DMS-2532394). 

• Co-organizer: Chris Eppolito 

• During Summer 2026, with support from the NSF LEAPS grant, I mentored two undergraduate summer research groups comprising a total of seven students (four from SUNY New Paltz and three from other institutions).

• One group investigated the prime ideals of B[x,y], where B denotes the Boolean semifield, as well as the topological and geometric properties of the prime congruences of B[x,y]. This project forms part of my broader research program on the commutative algebra of semirings.

• The second group investigated the following question: given a finite group G, what oriented matroid structures on G admit the property that left multiplication by every element of G induces an automorphism of the oriented matroid? This project builds on earlier work in tropical representation theory, where linear spaces are replaced by tropical linear spaces. In that setting, the analogous problem for ordinary matroids (rather than oriented matroids) arises naturally as a special case of the regular representation.

Participants (from the left)

• Catie Lillja (Johns Hopkins University)

• Nick Hannani (The College of New Jersey)

• Alex Norwood (SUNY New Paltz)

• Daisy Ivy Thackrah (SUNY New Paltz)

• Tristan Bishop (SUNY New Paltz)

• Radford Green (Johns Hopkins University)

• Jack Tiripicchio (SUNY New Paltz)