Feb 05, 2018
Monday

09:15 AM  09:30 AM


Welcome

 Location
 SLMath: Eisenbud Auditorium
 Video


 Abstract
 
 Supplements



09:30 AM  10:30 AM


Character theory of finite groups of Lie type
Meinolf Geck (Universität Stuttgart)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
In these lectures we provide an introduction to Lusztig's classification
of the irreducible characters of a finite group of Lie type. This essentially relies on
structural properties of the underlying algebraic group, which will be surveyed
in the first lecture. We then go on to discuss the partition of the set of characters
into series and the Jordan decomposition of characters. Finally, we address the
problem of computing character values, in the framework of Lusztig's theory of
character sheaves
 Supplements



10:30 AM  11:00 AM


Break

 Location
 SLMath: Eisenbud Auditorium
 Video


 Abstract
 
 Supplements



11:00 AM  12:00 PM


Characters of Finite Groups and Chains of psubgroups
Gabriel Navarro (University of Valencia)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
We will speak about the simplest of Dade's counting conjectures, and its relationship with the McKay and the Alperin Weight Conjecture
 Supplements



12:00 PM  02:00 PM


Lunch

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



02:00 PM  03:00 PM


Representation theory of reductive algebraic groups: techniques and applications
Donna Testerman (École Polytechnique Fédérale de Lausanne (EPFL))

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
The lectures will serve as an introduction to the representation theory of reductive linear algebraic groups,
with the goal of illustrating techniques and applications to some ongoing research problems.
Foundational material should include: highest weight theory and irreducible modules, Weyl modules
and induced modules, extension theory, dual modules, Steinberg tensor product theorem, restriction to Levi
factors, weight multiplicities.
The more advanced topics will be chosen from: applications to subgroup structure of reductive groups,
branching problems, and some current research directions.
 Supplements


03:00 PM  03:30 PM


Tea

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



03:30 PM  04:30 PM


Block theory of finite group algebras.
Radha Kessar (City University)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
The lectures will provide an introduction to the the theory of pblocks of finite groups . The emphasis will be on the interplay between plocal invariants and global structure
 Supplements




Feb 06, 2018
Tuesday

09:30 AM  10:30 AM


Monoidal categories and categorification
Jonathan Brundan (University of Oregon)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
In this series of talks, I will give an introduction to some of the ideas of “categorification” which have created a new point of view in representation theory centered around various monoidal categories of a diagrammatic nature. I will likely start by discussing classical examples such as the TemperleyLieb and HOMFLYPT skein categories, before focussing on the KacMoody 2category of Khovanov, Lauda and Rouquier. Many of the categories appearing in classical representation theory, especially of symmetric and general linear groups, admit additional structure making them into module categories (“2representations”) over the KacMoody 2category. This has consequences both at a combinatorial level (related to crystals and labelling sets of irreducible modules) and at a categorical level (related to the construction of Morita and derived equivalences between blocks)
 Supplements



10:30 AM  11:00 AM


Break

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



11:00 AM  12:00 PM


Character theory of finite groups of Lie type
Meinolf Geck (Universität Stuttgart)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
In these lectures we provide an introduction to Lusztig's classification
of the irreducible characters of a finite group of Lie type. This essentially relies on
structural properties of the underlying algebraic group, which will be surveyed
in the first lecture. We then go on to discuss the partition of the set of characters
into series and the Jordan decomposition of characters. Finally, we address the
problem of computing character values, in the framework of Lusztig's theory of
character sheaves."
 Supplements



12:00 PM  02:00 PM


Lunch

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



02:00 PM  03:00 PM


Representations of finite reductive groups: from characteristic zero to transverse characteristic
Olivier Dudas (Université de Paris VII (Denis Diderot))

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
This series of lectures will be centered on decomposition numbers for a special class of finite groups such as GL_n(q), SO_n(q),... E_8(q). I will first present what kind of numerical invariants decomposition numbers are, and what representationtheoretic problems they can solve. For finite reductive groups, I will explain how one can use DeligneLusztig theory to get basic sets of ordinary characters and to compute decomposition numbers. If time permits, I will mention a few open problems, including the case of small characteristic.
Lecture 1  Generalities on decomposition numbers
Lecture 2  Basic sets for finite reductive groups
Lecture 3  Computing decomposition numbers
 Supplements



03:00 PM  03:30 PM


Tea

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



03:30 PM  04:30 PM


Representation theory of reductive algebraic groups: techniques and applications
Donna Testerman (École Polytechnique Fédérale de Lausanne (EPFL))

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
The lectures will serve as an introduction to the representation theory of reductive linear algebraic groups,
with the goal of illustrating techniques and applications to some ongoing research problems.
Foundational material should include: highest weight theory and irreducible modules, Weyl modules
and induced modules, extension theory, dual modules, Steinberg tensor product theorem, restriction to Levi
factors, weight multiplicities.
The more advanced topics will be chosen from: applications to subgroup structure of reductive groups,
branching problems, and some current research directions.
 Supplements


04:30 PM  06:20 PM


Reception

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements




Feb 07, 2018
Wednesday

09:30 AM  10:30 AM


Characters of Finite Groups and Chains of psubgroups
Gabriel Navarro (University of Valencia)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
We will speak about the simplest of Dade's counting conjectures, and its relationship with the McKay and the Alperin Weight Conjecture
 Supplements



10:30 AM  11:00 AM


Break

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



11:00 AM  12:00 PM


Block theory of finite group algebras.
Radha Kessar (City University)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
The lectures will provide an introduction to the the theory of pblocks of finite groups . The emphasis will be on the interplay between plocal invariants and global structure
 Supplements




Feb 08, 2018
Thursday

09:30 AM  10:30 AM


Representation theory of reductive algebraic groups: techniques and applications
Donna Testerman (École Polytechnique Fédérale de Lausanne (EPFL))

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
The lectures will serve as an introduction to the representation theory of reductive linear algebraic groups,
with the goal of illustrating techniques and applications to some ongoing research problems.
Foundational material should include: highest weight theory and irreducible modules, Weyl modules
and induced modules, extension theory, dual modules, Steinberg tensor product theorem, restriction to Levi
factors, weight multiplicities.
The more advanced topics will be chosen from: applications to subgroup structure of reductive groups,
branching problems, and some current research directions.
 Supplements


10:30 AM  11:00 AM


Break

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



11:00 AM  12:00 PM


Representations of finite reductive groups: from characteristic zero to transverse characteristic
Olivier Dudas (Université de Paris VII (Denis Diderot))

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
This series of lectures will be centered on decomposition numbers for a special class of finite groups such as GL_n(q), SO_n(q),... E_8(q). I will first present what kind of numerical invariants decomposition numbers are, and what representationtheoretic problems they can solve. For finite reductive groups, I will explain how one can use DeligneLusztig theory to get basic sets of ordinary characters and to compute decomposition numbers. If time permits, I will mention a few open problems, including the case of small characteristic.
Lecture 1  Generalities on decomposition numbers
Lecture 2  Basic sets for finite reductive groups
Lecture 3  Computing decomposition numbers
 Supplements



12:00 PM  02:00 PM


Lunch

 Location
 SLMath: Eisenbud Auditorium
 Video


 Abstract
 
 Supplements



02:00 PM  03:00 PM


Monoidal categories and categorification
Jonathan Brundan (University of Oregon)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
In this series of talks, I will give an introduction to some of the ideas of “categorification” which have created a new point of view in representation theory centered around various monoidal categories of a diagrammatic nature. I will likely start by discussing classical examples such as the TemperleyLieb and HOMFLYPT skein categories, before focussing on the KacMoody 2category of Khovanov, Lauda and Rouquier. Many of the categories appearing in classical representation theory, especially of symmetric and general linear groups, admit additional structure making them into module categories (“2representations”) over the KacMoody 2category. This has consequences both at a combinatorial level (related to crystals and labelling sets of irreducible modules) and at a categorical level (related to the construction of Morita and derived equivalences between blocks)
 Supplements



03:00 PM  03:30 PM


Tea

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



03:30 PM  04:30 PM


Block theory of finite group algebras.
Radha Kessar (City University)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
The lectures will provide an introduction to the the theory of pblocks of finite groups . The emphasis will be on the interplay between plocal invariants and global structure.
 Supplements




Feb 09, 2018
Friday

09:30 AM  10:30 AM


Characters of Finite Groups and Chains of psubgroups
Gabriel Navarro (University of Valencia)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
We will speak about the simplest of Dade's counting conjectures, and its relationship with the McKay and the Alperin Weight Conjecture
 Supplements



10:30 AM  11:00 AM


Break

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



11:00 AM  12:00 PM


Representations of finite reductive groups: from characteristic zero to transverse characteristic
Olivier Dudas (Université de Paris VII (Denis Diderot))

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
This series of lectures will be centered on decomposition numbers for a special class of finite groups such as GL_n(q), SO_n(q),... E_8(q). I will first present what kind of numerical invariants decomposition numbers are, and what representationtheoretic problems they can solve. For finite reductive groups, I will explain how one can use DeligneLusztig theory to get basic sets of ordinary characters and to compute decomposition numbers. If time permits, I will mention a few open problems, including the case of small characteristic.
Lecture 1  Generalities on decomposition numbers
Lecture 2  Basic sets for finite reductive groups
Lecture 3  Computing decomposition numbers
 Supplements



12:00 PM  02:00 PM


Lunch

 Location
 SLMath: Atrium
 Video


 Abstract
 
 Supplements



02:00 PM  03:00 PM


Monoidal categories and categorification
Jonathan Brundan (University of Oregon)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
In this series of talks, I will give an introduction to some of the ideas of “categorification” which have created a new point of view in representation theory centered around various monoidal categories of a diagrammatic nature. I will likely start by discussing classical examples such as the TemperleyLieb and HOMFLYPT skein categories, before focussing on the KacMoody 2category of Khovanov, Lauda and Rouquier. Many of the categories appearing in classical representation theory, especially of symmetric and general linear groups, admit additional structure making them into module categories (“2representations”) over the KacMoody 2category. This has consequences both at a combinatorial level (related to crystals and labelling sets of irreducible modules) and at a categorical level (related to the construction of Morita and derived equivalences between blocks).
 Supplements



03:00 PM  03:30 PM


Tea

 Location
 
 Video


 Abstract
 
 Supplements



03:30 PM  04:30 PM


Character theory of finite groups of Lie type
Meinolf Geck (Universität Stuttgart)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
In these lectures we provide an introduction to Lusztig's classification
of the irreducible characters of a finite group of Lie type. This essentially relies on
structural properties of the underlying algebraic group, which will be surveyed
in the first lecture. We then go on to discuss the partition of the set of characters
into series and the Jordan decomposition of characters. Finally, we address the
problem of computing character values, in the framework of Lusztig's theory of
character sheaves."
 Supplements



