# Metric and Analytic Aspects of Moduli Spaces

Created: | 2015-07-29 16:24 |
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Institution: | Isaac Newton Institute for Mathematical Sciences |

Description: | The term moduli space has its origins in the classification of conformal structures on two-dimensional surfaces. Closed surfaces are classified topologically by their genus, but for fixed genus, the set of inequivalent conformal structures is essentially a smooth finite- dimensional manifold, a first example of a moduli space.
In more recent times, many other instances of mathematical structures of this type have come to light, above all in gauge theory. They have had, and continue to have, a major impact in modern geometry, topology and mathematical physics. Working with moduli spaces is subtle. First of all, they are implicitly defined (typically) as equivalence classes of solutions to some nonlinear partial differential equations. Second, they are almost invariably non-compact and/or singular, and one of the challenges is to understand them asymptotically and/or near the singularities. The goal of the programme is to explore moduli spaces from the metric and analytical points of view. We shall survey the current state of the art with a focus on four themes: 4-dimensional hyperKaehler manifolds; compactification of moduli spaces; analysis on moduli spaces; new constructions and challenges. There will be a 5-day workshop during the second week of the programme. |

# Media items

This collection contains 36 media items.

### Media items

#### Coulomb branches of 3-dimensional N=4 gauge theories

Nakajima, H (Kyoto University)

Wednesday 29 July 2015, 10:00-11:00

**Collection**:
Metric and Analytic Aspects of Moduli Spaces

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 4 Aug 2015

#### Hyperkähler toy models

Hausel, T (EPFL - Ecole Polytechnique Fédérale de Lausanne)

Thursday 30 July 2015, 09:00-10:00

**Collection**:
Metric and Analytic Aspects of Moduli Spaces

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 4 Aug 2015

#### Perverse sheaves on compactifications of locally symmetric spaces

Saper, LD (Duke University)

Tuesday 28 July 2015, 16:00-17:00

**Collection**:
Metric and Analytic Aspects of Moduli Spaces

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 31 Jul 2015

#### Quantization of integrable systems of periodic monopoles

Pestun, V (IHES)

Thursday 30 July 2015, 10:00-11:00

**Collection**:
Metric and Analytic Aspects of Moduli Spaces

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 4 Aug 2015

#### A construction of limiting solutions of Hitchin's equations

Fredrickson, L (University of Texas at Austin)

Wednesday 05 August 2015, 11:00-12:00

**Collection**:
Metric and Analytic Aspects of Moduli Spaces

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 11 Aug 2015

#### ALG and ALH spaces

Hein, H-J (University of Maryland)

Monday 20 July 2015, 16:00-17:00

**Collection**:
Metric and Analytic Aspects of Moduli Spaces

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 30 Jul 2015

#### ALG and the SU(∞) Toda equation

Hitchin, N (University of Oxford)

Wednesday 29 July 2015, 11:30-12:30

**Collection**:
Metric and Analytic Aspects of Moduli Spaces

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Wed 5 Aug 2015

#### An analytic construction of dihedral ALF gravitational instantons

Auvray, H (Université Paris-Sud)

Monday 27 July 2015, 11:30-12:30

**Collection**:
Metric and Analytic Aspects of Moduli Spaces

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 31 Jul 2015

#### Analysis on singular spaces

Albin, P (University of Illinois at Urbana-Champaign)

Wednesday 22 July 2015, 11:00-12:30

**Collection**:
Metric and Analytic Aspects of Moduli Spaces

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 30 Jul 2015

#### Asymptotically Conic Calabi-Yau Manifolds

Conlon, R (UQAM - Université du Québec à Montréal)

Wednesday 12 August 2015, 15:30-16:30

**Collection**:
Metric and Analytic Aspects of Moduli Spaces

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 14 Aug 2015

#### Asymptotics and compactification of monopole moduli space

Bielawski, R (Leibniz Universität Hannover)

Wednesday 29 July 2015, 09:00-10:00

**Collection**:
Metric and Analytic Aspects of Moduli Spaces

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 4 Aug 2015

#### Asymptotics of hyperboilic, Weil-Peterssen and Takhtajan-Zograf metrics

Melrose, R (Massachusetts Institute of Technology)

Tuesday 28 July 2015, 11:30-12:30

**Collection**:
Metric and Analytic Aspects of Moduli Spaces

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 31 Jul 2015

#### Coulomb Branch and the Moduli Space of Instantons

Hanany, A (Imperial College London)

Friday 31 July 2015, 11:30-12:30

**Collection**:
Metric and Analytic Aspects of Moduli Spaces

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 4 Aug 2015

#### Decay and Moduli of Yang Mills Instantons

Stern, M (Duke University)

Tuesday 21 July 2015, 15:30-16:30

**Collection**:
Metric and Analytic Aspects of Moduli Spaces

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 30 Jul 2015

#### Folded hyperKähler metrics

Biquard, O (École Normale Supérieure)

Monday 27 July 2015, 10:00-11:00

**Collection**:
Metric and Analytic Aspects of Moduli Spaces

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Thu 30 Jul 2015

#### Higgs bundles, spectral data, and fiber products of curves

Bradlow, S (University of Illinois)

Tuesday 04 August 2015, 11:00-12:00

**Collection**:
Metric and Analytic Aspects of Moduli Spaces

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 11 Aug 2015

#### HyperKaehler metrics with circle action

Swann, A (Aarhus Universitet)

Wednesday 12 August 2015, 14:00-15:00

**Collection**:
Metric and Analytic Aspects of Moduli Spaces

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 14 Aug 2015

#### Kähler metrics and Chern forms on the moduli space of punctured Riemann surfaces

Takhtajan, LA (Stony Brook University)

Monday 27 July 2015, 16:00-17:00

**Collection**:
Metric and Analytic Aspects of Moduli Spaces

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 31 Jul 2015

#### Mass in Kaehler Geometry

LeBrun, C (Stony Brook University)

Friday 31 July 2015, 10:00-11:00

**Collection**:
Metric and Analytic Aspects of Moduli Spaces

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Tue 4 Aug 2015

#### Moduli space of periodic monopoles and Hitchin equations on a cylinder

Maldonado, R (University of Cambridge)

Tuesday 11 August 2015, 14:00-15:00

**Collection**:
Metric and Analytic Aspects of Moduli Spaces

**Institution**:
Isaac Newton Institute for Mathematical Sciences

**Created**:
Fri 14 Aug 2015