## Departmental Ph.D. Thesis Exam – Saied Sorkhou

Tuesday, April 5, 2022 at 2:00 p.m. (sharp)

PhD Candidate: Saied Sorkhou
Supervisor: Joe Repka
Thesis title: Levi Decomposable Subalgebras of Classical Lie Algebras with Regular
Simple Levi Factor

***

This thesis describes and characterizes a significant class of subalgebras of the classical Lie algebras, namely those which are Levi decomposable with regular and simple Levi factor, with select exceptions. Such subalgebras are entirely determined by their Levi factors and radicals. The possible Levi factors are well-established in the literature and so the contribution of this thesis is a characterization of the radicals. The radicals naturally decompose into nontrivial and trivial components. The nontrivial component is found to be fully classified by subsets of the parent root system and Weyl group. However, a classification of the trivial component requires solving the open problem of classifying solvable subalgebras of classical Lie algebras. Nonetheless, this thesis establishes a criterion on the trivial components for determining when two such subalgebras are conjugate. This thesis also briefly explores the ramifications of relaxing
simplicity of the Levi factor to allow for semisimplicity.

***

A draft of the thesis is available here: thesis_draft_Feb_23_2022

## September 2013 Comprehensive Exam Schedule

The September 2013 PhD Comprehensive Exam schedule is as follows:

Wednesday, September 4, 2013, 1-4 p.m., in BA 6183
Analysis (real and complex) PhD Comprehensive Exam
There is the option of writing only the real questions (2 hour exam)
or the complex questions only (1.5 hour exam).

Thursday, September 5, 2013, 1-4 p.m., in BA 6183
Algebra PhD Comprehensive Exam

Friday, September 6, 2013, 10:00 a.m.-1:00 p.m., in BA 6183
Topology PhD Comprehensive Exam

Ph.D. students must pass all their comprehensive exams within 12 months of
entering the program (i.e. by the September sitting of the second year).

Please inform Jemima (jmerisca@math) if you wish to write one or
more of the above exams.

Past comprehensive exam questions can be viewed at:
http://www.math.toronto.edu/graduate/pce/

## 2013 Probability Comprehensive Exam

The Statistics Department has scheduled their annual Probability
Comprehensive Exam on:

Friday, May 31, 2013, 12:00 to 5:00 p.m., in SS1088, 100 St. George St.

If you plan to take this exam as one of your three required PhD comprehensive exams,

Thanks,

Jemima

## September 2012 PhD Comprehensive Exam Schedule

The September 2012 PhD Comprehensive Exam schedule is as follows:

Wednesday, September 5, 2012, 1-4 p.m., in BA 6183
Analysis (real and complex) PhD Comprehensive Exam
There is the option of writing only the real questions (2 hour exam)
or the complex questions only (1.5 hour exam).

Thursday, September 6, 2012, 1-4 p.m., in BA 6183
Algebra PhD Comprehensive Exam

Friday, September 7, 2012, 10 am - 1 p.m., in BA 6183
Topology PhD Comprehensive Exam

Ph.D. students must pass all their comprehensive exams within
12 months of entering the program (i.e. by the September
sitting of the second year).

Please inform Ida (ida@math) if you wish to write one or more
of the above exams.

Past comprehensive exam questions can be viewed at
http://www.math.toronto.edu/graduate/pce/

## Mathematical Finance Comprehensive Exam

We plan to have a sitting of the mathematical finance PhD qualifying
exam in the next month or two.  If you are interested in this field
for your PhD studies and want to write this exam, please let me know
as soon as possible.  The other two qualifying exams must be from
the core areas of analysis, algebra, topology or pde's.

The syllabus for this exam can be found on page 28 of the
2011-12 Graduate Studies in Mathematis Handbook:

Ida

## Probability Comprehensive Exam

The Statistics Department has scheduled their annual Probability
Comprehensive Exam on

Wednesday, May 30, 2012, 12-5 p.m., in SS1078, 100 St. George St.

If you plan to take this exam as one of your three required PhD
comprehensive exams, please let me know and I will pass on your
name to the Statistics graduate office.

Thanks,

Ida

## Core Course Exam Schedule and Complex Analysis Comprehensive Exam

Students can view the scheduling of this semester's
core course exams on the graduate timetable:

For students not registered in the complex analysis core course
but would like to take the final exam for PhD comprehensive exam
credit, please let me know.  You will write the exam on the same
day and time (Wednesday, April 18, 2012, 2-5 pm) but not with the class.
Please come to my office before the exam and I will settle you into
a room to write the exam.

Good luck to all writing exams.

Ida

## September 2011 PhD Comprehensive Exams

The September 2011 PhD Comprehensive Exam schedule is
as follows:

Wednesday, September 7, 2011, 1-4 p.m., in BA 6183
Analysis (real and complex) PhD Comprehensive Exam
There is the option of writing only the real questions (2 hour exam)
or the complex questions only (1.5 hour exam).

Thursday, September 8, 2011, 1-4 p.m., in BA 6183
Algebra PhD Comprehensive Exam

Friday, September 9, 2011, 10 am - 1 p.m., in BA 6183
Topology PhD Comprehensive Exam

Ph.D. students must pass all their comprehensive exams within
12 months of entering the program (i.e. by the September
sitting of the second year).

Please inform Ida (ida@math) if you wish to write one or more
of the above exams.

Past comprehensive exam questions can be viewed at
http://www.math.toronto.edu/graduate/pce/