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--- seminars:colloquium [2025/10/31 15:16]
adrian
+++ seminars:colloquium [2025/11/03 14:38] (current)
qiao
@@ Line 1: / Line 1: @@
 ====== Colloquium ======
-Unless stated otherwise, colloquia are scheduled for Thursdays 4:15-5:15pm in WH-100E with refreshments served from 4:00-4:15 pm in WH-102.
+Unless stated otherwise, colloquia are scheduled for Thursdays 4:00-5:00pm in WH-100E with refreshments served from 3:45-4:00 pm in WH-102.
 Organizers: [[people:dobbins:start]], [[people:kargin:start|Vladislav Kargin]], [[people:malkiewich:start]],
@@ Line 15: / Line 15: @@
 <WRAP box 90%>
 **//Abstract//**:
-TBA\\
+Whenever a mathematical object is given in
+characteristic p, one can ask whether it is the reduction, in some
+sense, of an analogous structure in characteristic zero.  If so, the
+structure in characteristic zero is called a "lift" of the structure
+in characteristic p.  The most famous example is Hensel's Lemma about
+lifting solutions of polynomials in Z/p to solutions in the p-adic
+integers Z_p.
+The “lifting problem” we consider is more geometric: given a smooth curve X in
+characteristic p with an action of a finite group G, is there a curve
+in characteristic zero with G-action that reduces to X?  Unsurprisingly, the answer is related to the group theory of G (for instance, if p does not divide |G| or if G is cyclic, then the curve with the G-action always lifts, but if G has an abelian, non-cyclic, non-p-subgroup that fixes a point on X, then the curve does not lift with the action).  After giving an introduction to the lifting problem and some examples, we will discuss well-established ways that the problem interacts with group theory, as well as more recent advances relating the problem to representation theory.\\
 </WRAP>

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