Mathematical Sciences

Departmental Weekly Events

October 18 – October 22, 2021



Monday, October 18

  • Algebra Seminar, Unary-determined distributive l-magmas., Peter Jipsen. 12:30PM. Link: 976 2397 3071

Abstract: A distributive lattice-ordered magma (dl-magma) (A,^,v,⬝) is a distributive lattice with a binary operation⬝ that preserves joins in both arguments, and when ⬝ is associative then (A,v,⬝) is an idempotent semiring. A dl-magma with a top T is unary-determined if xy = (xT ^ y) v (x ^ Ty). These algebras are term-equivalent to a subvariety of distributive lattices with T and two join-preserving unary operations p,q. We obtain simple conditions on p,q such that xy = (p(x) ^ y) v (x ^ q(y)) is associative, commutative, idempotent and/or has an identity element. Furthermore, we show that a dl-magma with a Boolean lattice reduct and idempotent ⬝ (xx=x) is always unary-determined. 

This generalizes previous results on the structure of doubly idempotent semirings and, in the case when the distributive lattice is a Heyting algebra, it provides structural insight into unary-determined residuated lattices that are algebraic models of bunched implication logic. We also provide Kripke semantics for the algebras under consideration, which leads to more efficient algorithms for constructing finite models. 

These results are joint work with Natanael Alpay and Melissa Sugimoto.


  • Statistics Seminar, The APP for estimating population proportion based on skew normal approximations and the Beta-Bernoulli process., Dr. Cong Wang, University of Nebraska Omaha. 3:30PM – 4:30PM. Link: 934 8064 2776


Tuesday, October 19

  • No events 


Wednesday, October 20

  • Tenure-Track Faculty Meeting, John Harding., 12:30PM – 1:30PM. Link: 937 1499 9334


Thursday, October 21

  • Foundations Seminar, Guram Bezhanishvili., 4:30PM – 5:30PM. Link: 955 8066 2273


Friday, October 22

  • Probability Seminar, An Introduction to Large Deviations with a View to the Lamperti Problem, PART 5., Robert Smits. 9AM – 10AM, Room SH 235. For those who want to join via Zoom: 972 0915 9954


  • Colloquium, Primary decomposition with differential operators., Yairon Cid-Ruiz, Ghent University. 12:05PM - 12:30PM online chat, 12:30PM - 1:30PM talk: 980 8999 6443

Abstract: We introduce differential primary decompositions for ideals in a commutative ring. Ideal membership is characterized by differential conditions. The minimal number of conditions needed is the arithmetic multiplicity. Minimal differential primary decompositions are unique up to change of bases. Our results generalize the construction of Noetherian operators for primary ideals in the analytic theory of Ehrenpreis-Palamodov, and they offer a concise method for representing affine schemes. The case of modules is also addressed. This is joint work with Bernd Sturmfels.


  • Biweekly Graduate Seminar, Next seminar November 5th. 


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  • Grad. School phone number: (575) 646–5746


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