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Now showing items 1-10 of 29

#### Coupling sparse models and dense extremal problems

(Massachusetts Institute of Technology, 2020)

We study the problem of coupling a stochastic block model with a planted bisection to a uniform random graph having the same average degree. Focusing on the regime where the average degree is a constant relative to the ...

#### K-theoretic Hall algebras for quivers with potential

(Massachusetts Institute of Technology, 2020)

Given a quiver with potential (Q, W), Kontsevich-Soibelman constructed a Hall algebra on the cohomology of the stack of representations of (Q, W). As shown by Davison-Meinhardt, this algebra comes with a filtration whose ...

#### Convergence of complete Ricci-βat manifolds

(Massachusetts Institute of Technology, 2020)

This thesis is focused on the convergence at inαnity of complete Ricci βat manifolds. In the αrst part of this thesis, we will give a natural way to identify between two scales, potentially arbitrarily far apart, in the ...

#### Stable characters for symmetric groups and wreath products

(Massachusetts Institute of Technology, 2020)

Given a Hopf algebra R, the Grothendieck group of C = R-mod inherits the structure of a ring. We define a ring [mathematical equation]), which is "the [mathematical equation] limit" of the Grothendieck rings of modules for ...

#### Assorted results in boolean function complexity, uniform sampling and clique partitions of graphs

(Massachusetts Institute of Technology, 2020)

This thesis consists of three disparate parts. In the first, we generalize and extend recent ideas of Chiarelli, Hatami and Saks to obtain new bounds on the number of relevant variables for a boolean function in terms of ...

#### Combinatorics of affine Springer fibers and combinatorial wall-crossing

(Massachusetts Institute of Technology, 2020)

This thesis deals with several combinatorial problems in representation theory. The first part of the thesis studies the combinatorics of affine Springer fibers of type A. In particular, we give an explicit description of ...

#### On the higher Frobenius

(Massachusetts Institute of Technology, 2020)

Given a homotopy invariant of a space, one can ask how much of the space can be recovered from that invariant. This question was first addressed in work of Quillen and Sullivan on rational homotopy theory in the 1960's and ...

#### Affine Springer fibers and the representation theory of small quantum groups and related algebras

(Massachusetts Institute of Technology, 2020)

This thesis deals with the connections of Geometry and Representation Theory. In particular we study the representation theory of small quantum groups and Frobenius kernels and the geometry of an equivalued affine Springer ...

#### An Orientation map for height p - 1 real E theory

(Massachusetts Institute of Technology, 2020)

Let p be an odd prime and let EO = E[superscript hC] [subscript p-1] be the Cp αxed points of height p - 1 Morava E theory. We say that a spectrum X has algebraic EO theory if the splitting of K[subscript *](X) as an ...

#### Computability of rational points on curves over function fields in characteristic p

(Massachusetts Institute of Technology, 2020)

The motivating problem of this thesis is that of explicitly computing the K-rational points of a regular nonsmooth curve X over a αnitely generated αeld K of characteristic p. We start with an in-depth study of such curves ...