Relating test ideals and multiplier ideals
August 8 to August 12, 2011
at the
American Institute of Mathematics,
San Jose, California
organized by
Karl Schwede and Kevin Tucker
Original Announcement
This workshop will be devoted to the the connection between two
prominent and distinct means of measuring singularities:
the multiplier ideal in complex algebraic geometry, and
the test ideal in positive characteristic commutative algebra. These two concepts are related via "reduction to characteristic p" techniques. The subsequent interplay of geometric methods in
characteristic zero and Frobenius techniques in positive characteristic continues to inspire new questions and results throughout numerous
areas of mathematics, including algebraic geometry, commutative algebra,
representation theory, and number theory.
Potential focus topics of this workshop include recent progress, new applications,
and remaining open questions in the following areas:

Understanding Fjumping numbers of test ideals as the
characteristic p > 0 varies.
 Computing test ideals via finite extensions and regular
alterations.

Test ideals and multiplier ideals in nonQGorenstein rings.
These topics relate to several major open conjectures, namely weak
verses strongly Fregularity, the direct summand conjecture and
questions of ordinarity versus supersingularity for higher dimensional
varieties.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
Papers arising from the workshop:
Depth of Fsingularities and base change of relative canonical sheaves
by Zsolt Patakfalvi and Karl Schwede,
J. Inst. Math. Jussieu 13 (2014), no. 1, 4363 MR3134015Semipositivity in positive characteristics
by Zsolt Patakfalvi,
Ann. Sci. Éc. Norm. Supér. (4) 47 (2014), no. 5, 9911025 MR3294622HilbertKunz functions of 2 x 2 determinantal rings
by Lance Edward Miller and Irena Swanson,
Illinois J. Math. 57 (2013), no. 1, 251277 MR3224570A Frobenius variant of Seshadri constants
by Mircea Mustata and Karl Schwede,
Math. Ann. 358 (2014), no. 34, 861878 MR3175143