Main lecture

The Main Step ( Lecture 12 )

Throughout this lecture, we let k denote an algebraically closed field, a prime number which is invertible in k, and X an algebraic curve over k. We begin by recalling a variant of a construction from the previous lecture.

6.440 Essential Coding Theory Lecture 18 1 Notations and Main Results from Last Lecture

Let G = L ∪ R be a bipartite graph with n left vertices and m right vertices. Then G corresponds to a binary code CG with block length n, and dimension k ≥ n −m, where the left vertices correspond to variables x1, . . . , xn ∈ {0, 1}, while the right vertices c1, . . . , cm correspond to constraints, such that ci is satisfied iff ∑ u↔ci xu = 0. Let SAT be the set of satisfied constraints, and U...

Tracks of a non-main path traveler: 2011 Thomas Willis Lecture.

After an unconventional beginning in stroke research, I veered off the main path repeatedly to view problems from a different perspective. In this lecture summary, I would like to return to several points along the byways that led to research with some continuity.

Lecture 2: Cm Types, Reflex Fields, and Main Theorem (2/22/12) Notes by I. Boreico

Recall the setting at the end of the previous lecture: A is an abelian variety over a field F of characteristic zero, with dimension g > 0. Let L be a number field of degree 2g over Q “acting” on A; that is, we have an embedding L ↪→ End(A). The elements of L that actually act on A – i.e., O := L ⋂ End(A) – form an order in L. Since char(F ) = 0, the action of O on T0(A) (a g-dimensional F -vec...

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