Triangle Seminars
Tuesday, 16 Feb 2016
Yang-Mills Theory and the ABC Conjecture
Yang-Hui He
(City)
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.
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.
Posted by: KCL
Wednesday, 17 Feb 2016
Topological quantum field theory: symmetries and defects
📍 London
Nils Carqueville
(Schroedinger Inst., Vienna)
Abstract:
A major paradigm of 20th-century science is to understand nature in the language of quantum field theory. Efforts to answer foundational questions about this language have led to successful and ongoing cross-fertilisation between theoretical physics and pure mathematics. In particular, Atiyah and Segal proposed an axiomisation of the path integral by beautifully linking geometry with algebra.
The talk starts with a lightening review of this functorial approach, and then quickly restricts to the case in which spacetime is two-dimensional and has no geometric structure: two-dimensional topological quantum field theory (TQFT). This seemingly simple situation is still surprisingly rich, and we will see how algebras, categories, and "higher" structures appear naturally; examples of such structures are ubiquitous in theoretical physics, string theory, and many areas of mathematics.
Once the stage is carefully set, we turn to the central notion of symmetry, which involves the action of groups on a TQFT. We will be led to interpret symmetries as special kinds of "defects" of the TQFT, which in turn allows for a natural, purely algebraic generalisation of orbifolding. This leads to new equivalences between TQFTs, of which we will discuss the examples of Landau-Ginzburg models, and (if time permits) refined knot invariants.
A major paradigm of 20th-century science is to understand nature in the language of quantum field theory. Efforts to answer foundational questions about this language have led to successful and ongoing cross-fertilisation between theoretical physics and pure mathematics. In particular, Atiyah and Segal proposed an axiomisation of the path integral by beautifully linking geometry with algebra.
The talk starts with a lightening review of this functorial approach, and then quickly restricts to the case in which spacetime is two-dimensional and has no geometric structure: two-dimensional topological quantum field theory (TQFT). This seemingly simple situation is still surprisingly rich, and we will see how algebras, categories, and "higher" structures appear naturally; examples of such structures are ubiquitous in theoretical physics, string theory, and many areas of mathematics.
Once the stage is carefully set, we turn to the central notion of symmetry, which involves the action of groups on a TQFT. We will be led to interpret symmetries as special kinds of "defects" of the TQFT, which in turn allows for a natural, purely algebraic generalisation of orbifolding. This leads to new equivalences between TQFTs, of which we will discuss the examples of Landau-Ginzburg models, and (if time permits) refined knot invariants.
Posted by: KCL
Charge-hyperscaling violating Lifshitz hydrodynamics from black-holes
Yoshinori Matsuo
(Crete)
Abstract:
Non-equilibrium black hole horizons are considered in scaling theories
with generic Lifshitz invariance and an unbroken U(1) symmetry.
There is also charge-hyperscaling violation
associated with a non-trivial conduction exponent.
The boundary stress tensor is computed and renormalized
and the associated hydrodynamic equations derived.
Upon a non-trivial redefinition of boundary sources associated
with the U(1) gauge field, the equations are mapped to
the standard non-relativistic hydrodynamics equations
coupled to a mass current and an external Newton potential
in accordance with the general theory of [arXiv:1502.00228].
The shear viscosity to entropy ratio is the same as in the relativistic case.
Non-equilibrium black hole horizons are considered in scaling theories
with generic Lifshitz invariance and an unbroken U(1) symmetry.
There is also charge-hyperscaling violation
associated with a non-trivial conduction exponent.
The boundary stress tensor is computed and renormalized
and the associated hydrodynamic equations derived.
Upon a non-trivial redefinition of boundary sources associated
with the U(1) gauge field, the equations are mapped to
the standard non-relativistic hydrodynamics equations
coupled to a mass current and an external Newton potential
in accordance with the general theory of [arXiv:1502.00228].
The shear viscosity to entropy ratio is the same as in the relativistic case.
Posted by: IC
Brane Brick Models, Toric Calabi-Yau 4-folds and 2d (0,2) Quivers
📍 London
Rak-Kyeong Seong
(KIAS)
Abstract:
In this talk, I will discuss Type IIA brane configurations consisting
of D4-branes suspended between NS5-branes which represent a large
class of 2d (0,2) quiver gauge theories. We call these new
constructions Brane Brick models. These are T-dual to D1-branes over
singular toric Calabi-Yau 4-folds and encode information about the
probed Calabi-Yau geometry as well as the corresponding GLSM. If time
permits, I will present how Brane Brick models naturally realise in
terms of a brane configuration 2d (0,2) Gadde-Gukov-Putrov triality.
In this talk, I will discuss Type IIA brane configurations consisting
of D4-branes suspended between NS5-branes which represent a large
class of 2d (0,2) quiver gauge theories. We call these new
constructions Brane Brick models. These are T-dual to D1-branes over
singular toric Calabi-Yau 4-folds and encode information about the
probed Calabi-Yau geometry as well as the corresponding GLSM. If time
permits, I will present how Brane Brick models naturally realise in
terms of a brane configuration 2d (0,2) Gadde-Gukov-Putrov triality.
Posted by: KCL
Thursday, 18 Feb 2016
Collabor8 - A Meeting for Early Career Researchers in Mathematical and Theoretical Physics
Various Various
(Various)
Abstract:
Collabor8 is a day-long meeting for early career researchers in mathematical and theoretical physics on Thursday 18th February 2016. The purpose of the meeting is to encourage collaboration between PhD students and postdocs from different institutions and research specialisms working in the UK.
The meeting will feature short presentations from selected speakers about ongoing research problems, in contrast to traditional longer seminars on completed work. These will form the basis of group discussions, where participants may share their expertise and suggest new approaches. The conference website provides a convenient social network to promote continuing interaction after the meeting.
We are delighted that Professor Luis Fernando Alday will be delivering a keynote lecture at the meeting. There is no conference fee, and funds are available to reimburse travel expenses.
Further information about the meeting, including the registration form, may be found on the website below. The deadline for registration is Thursday 4th February.
http://www.collabor8research.org
Collabor8 is a day-long meeting for early career researchers in mathematical and theoretical physics on Thursday 18th February 2016. The purpose of the meeting is to encourage collaboration between PhD students and postdocs from different institutions and research specialisms working in the UK.
The meeting will feature short presentations from selected speakers about ongoing research problems, in contrast to traditional longer seminars on completed work. These will form the basis of group discussions, where participants may share their expertise and suggest new approaches. The conference website provides a convenient social network to promote continuing interaction after the meeting.
We are delighted that Professor Luis Fernando Alday will be delivering a keynote lecture at the meeting. There is no conference fee, and funds are available to reimburse travel expenses.
Further information about the meeting, including the registration form, may be found on the website below. The deadline for registration is Thursday 4th February.
http://www.collabor8research.org
Posted by: QMW