Tuesday, August 23 2022 at 3:00 p.m. (sharp)

MSc Candidate: Mahmud Azam

Supervisor: Alexander Kupers

Thesis title: Semidirect Products of ∞–Operads

***

We provide a construction of an $\infty$–operad from a functor $BG \to \Op_\infty$ encoding the action of a group $G$ on a given unital $\infty$–operad whose underlying $\infty$–category is a Kan complex. This construction, restricted to classical operads in $\Set$ viewed as $\infty$–operads, coincides with the semidirect product construction. Taking this as the definition of semidirect product of $\infty$–operads, we show that the action of $G$ on the given $\infty$–operad is equivalent to the trivial action if and only if the corresponding semidirect products

are equivalent. We then outline how one might generalize this result to operads in $\Top$

and use this to show that the semidirect product of the real version of the little $n$–disks operad with $SO(n – 1)$ or $SO(n – 2)$ for $n$ even or odd respectively corresponding to the usual action is equivalent to the semidirect product corresponding to the trivial action.

***

A copy of the thesis can be found here:Operads

exam
Students can view the scheduling of this semester's
core course exams on the graduate timetable:
http://www.math.toronto.edu/cms/2011-2012-graduate-course-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

exam, graduate course, PhD Comprehensive Exams
Hello,
This is just a quick reminder of the PhD comprehensive exams
taking place next week. They are as follows:
Analysis: Wednesday, September 7, 2011, 1-4 pm, in BA 6183
(the real only exam is 2 hours, the complex only exam
is 1.5 hours)
Algebra: Thursday, September 8, 2011, 1-4 pm, in BA 6183
Topology: Friday, September 9, 2011, 10 am - 1 pm, in BA 6183
If you have not signed up and would like to write one or more
exams, please let me know.
Thanks and good luck to all who are writing.
Ida

Comprehensives, exam
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/

exam, PhD Comprehensive Exams
The Probability Theory comprehensive exam is administered by
the Department of Statistics and is always held in May.
Math students may choose to write this exam and use it as
one of the three PhD comprehensive exam requirements for our
program. It is not enough to take the Probability Theory courses
(STA 2111HF and STA 2211HS) and obtain the minimum grade of A-,
as is done with our core material.
The exam is an almost all-day affair and this year it will be held
on Tuesday, May 24, 2011.
Please let me know asap if you intend to register for the exam.
I will then pass your name on to the Statistics Dept.
Thanks,
Ida

announcement, exam, Exam PhD
Please note the new date for the final exam of
MAT 1101HS - Algebra II
Instructor: Paul Selick
New Date: TUESDAY, APRIL 19, 2011
Time: 2-5 p.m.
Location: BA 6183

announcement, exam
Not all graduate courses will have final exams, but some do and
I have listed the ones that have I helped organize or that have
been scheduled by the Faculty of Arts and Science, i.e. the cross-
listed courses. Updates will be e-mailed to you and I will list
the dates and times of the exams also on the grad timetable:
http://www.math.toronto.edu/cms/tentative-2010-2011-graduate-course-schedule/
If you are not registered in a core course and you wish to obtain
partial comprehensive credit by writing the final exam, please let
me know.
****
Real Analysis II (MAT 1001HS / MAT 458H1S)
Tuesday, April 26, 2011, 2-5 p.m., in HI-CART
Cartwright Hall, St. Hilda's College, 44 Devonshire Place
****
Complex Analysis (MAT 1002HS / MAT 454H1S)
Wednesday, April 20, 2011, 9 a.m. - 12 noon, in WI 1017
Wilson Hall, New College, 40 Willcocks Street (east of Spadina Avenue)
****
Algebra II (MAT 1101HS)
~~Wednesday, April 20, 2011~~, 2-5 p.m., in BA 6183
Tuesday, April 19, 2011
****
General Relativity (MAT 1700HS / APM 426H1S)
Thursday, April 28, 2011, 2-5 p.m., in EX 300
Central Exams Facility, 255 McCaul St. (just south of College St.)
****
Combinatorial Methods (MAT 1302HS / APM 461H1S)
Wednesday, April 13, 2011, 7-10 p.m., in BN3
Upper Small Gymnasium, Benson Building, 320 Huron Street
(south of Harbord Street), Third Floor

announcement, exam
Students, who are not registered in a core course but wish to
take a core course exam for partial
PhD comprehensive exam credit, should let me know immediately!
Thanks.
Please note that I have updated the grad timetable with the
schedule of this semester's grad course final exams.
Nonetheless, here is the schedule:
MAT 1000HF - Real Analysis I
Friday, December 17, 2010, 9 am - 12 noon, in BN 3,
Upper Small Gymnasium, Benson Building, 320 Huron St., 3rd Floor
MAT 1060HF - PDE I
Friday, December 10, 2010, 10 am - 2 pm, in BA 2135, 40 St. George St.
MAT 1100HF - Algebra I
Tuesday, December 14, 2010, 10 am - 1 pm, in BA 6183, 40 St. George St.
MAT 1300HF - Topology I
Wednesday, December 15, 2010, 2 - 5 pm, in BA 6183, 40 St. George St.
MAT 1723HF - Quantum Mechanics
Monday, December 20, 2010, 9 am - 12 noon, in BR200,
Brennan Hall, St. Michael's College, 81 St. Mary St.
Good luck to all writing!

announcement, exam