Found 10 result(s)

### 16.02.2016 (Tuesday)

#### Yang-Mills Theory and the ABC Conjecture

Regular Seminar Yang-Hui He (City)

 at: 15:00 City U.room B103 abstract: We establish a precise correspondence between the ABC Conjecture and N=4 super-Yang-Mills theory. This is achieved by combining three ingredients: (i) Elkies' method of mapping ABC-triples to elliptic curves in his demonstration that ABC implies Mordell/Faltings; (ii) an explicit pair of elliptic curve and associated Belyi map given by Khadjavi-Scharaschkin; and (iii) the fact that the bipartite brane-tiling/dimer model for a gauge theory with toric moduli space is a particular dessin d'enfant in the sense of Grothendieck. We explore this correspondence for the highest quality ABC-triples as well as large samples of random triples. The Conjecture itself is mapped to a statement about the fundamental domain of the toroidal compactification of the string realization of N=4 SYM.

### 26.11.2015 (Thursday)

Regular Seminar Yang-Hui He (City)

 at: 14:00 QMWroom G.O. Jones 610 abstract: We study the web of correspondences linking the exceptional Lie algebras E8,7,6 and the sporadic simple groups Monster, Baby and the largest Fischer group. We will survey some old observations from the perspective of Moonshine and representation theory and present some new ones from that of congruence groups and enumerative geometry. Based on joint work with John McKay.

### 10.12.2014 (Wednesday)

#### Eta Products, BPS States and K3 Surfaces

Regular Seminar Yang-Hui He (City University)

 at: 13:15 KCLroom G.01 abstract: Inspired by the multiplicative nature of the Ramanujan modular discriminant, Delta, we consider physical realizations of certain multiplicative products over the Dedekind eta-function in two parallel directions: the generating function of BPS states in certain heterotic orbifolds and elliptic K3 surfaces associated to congruence subgroups of the modular group. We show that they are, after string duality to type II, the same K3 surfaces admitting Nikulin automorphisms. In due course, we will present some identities arising from q-expansions as well as relations to the sporadic Mathieu group M24.

### 03.12.2014 (Wednesday)

#### Polygon Seminar: Gauge Theories and Calabi-Yau Manifolds

Triangular Seminar Yang-Hui He (City University)

 at: 15:30 QMWroom Francis Bancroft 1.15 abstract:

### 21.03.2014 (Friday)

#### TBA

Regular Seminar Yang-Hui He (City U.)

 at: 14:00 QMWroom Room FB 1.06 abstract:

### 19.03.2012 (Monday)

#### N=2 Gauge Theories: Congruence Subgroups, Coset Graphs and Modular Surfaces

Regular Seminar Yang-Hui He (City University)

 at: 13:00 ICroom H341 abstract: We establish a correspondence between generalized quiver gauge theories in four-dimensions and congruence subgroups of the modular group, hinging upon the trivalent graphs which arise in both. The gauge theories and the graphs are enumerated and their numbers are compared. The correspondence is particularly striking for genus zero torsion-free congruence subgroups which are crucial to Moonshine. We analyze in detail the case of index 24, where modular elliptic K3 surfaces emerge: here, the elliptic j-invariants can be recast as dessins d'enfant which dictate the Seiberg-Witten curves.

### 16.03.2010 (Tuesday)

#### A Geometric Apercu on N=1 Gauge Theories

Regular Seminar Yang-Hui He (Oxford University)

 at: 13:30 City U.room Oakden abstract: We present some new perspectives on N=1 gauge theories, especially SQCD, D-Brane Quiver Theories and the MSSM, from the stand-point of recent advances in computational and algorithmic algebraic geometry and commutative algebra. We introduce the plethystic program which systematically count gauge invariants and encodes certain hidden symmetries. Moreover, we discuss special structures of the vacuum moduli space, such as that of SQCD being Calabi-Yau.

### 12.03.2008 (Wednesday)

#### Triadophilia: A Special Corner in the Landscape

Regular Seminar Yang-Hui He (Oxford University)

 at: 14:00 ICroom Huxley 503 abstract: We point out a special corner in the space of Calabi-Yau compactifications where standard-like models tend to emerge. We show how these scenarios are inter-related via a mathematical process of transgression of bundles, a generalisation of the conifold transition. Perhaps our world is special and we live in this oasis within the multitude of vacua.

### 06.03.2006 (Monday)

#### Heterotic MSSM

Regular Seminar Yang-Hui He (Oxford)

 at: 13:30 ICroom Ballroom, 58 Princes Gate abstract: We show the existence of an N=1 supersymmetric vacuum in string theory whose observable sector has exactly the matter content of the MSSM without exotic particles and vector-like pairs of any type. This is done so by compactifying the E_8 x E_8 heterotic string on a Calabi-Yau threefold endowed with an SU(4) vector bundle which has been constructed after extensive search. In addition, we discuss the Yukawa couplings and Higgs mu-terms in this model.

### 10.11.2004 (Wednesday)

#### GUT spectrum from Heterotic Compactification

Regular Seminar Yang-Hui He (University of Pennsylvania)

 at: 13:15 KCLroom 423 abstract: