
Tue 8 Sep 2015, 9:00am
SPECIAL
One Time Event
Math 125

Qualifying Exams  Analysis

Math 125
Tue 8 Sep 2015, 9:00am12:00pm
Details
For more information on Qualifying Exams, please visit http://www.math.ubc.ca/Grad/QualifyingExams/index.shtml
Lunch will be provided in Math 125 for students writing the Analysis exam.
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Tue 8 Sep 2015, 1:00pm
SPECIAL
One Time Event
Math 125

Qualifying Exams  Algebra

Math 125
Tue 8 Sep 2015, 1:00pm4:00pm
Details
For more info, please visit http://www.math.ubc.ca/Grad/QualifyingExams/index.shtml
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Tue 8 Sep 2015, 1:00pm
SPECIAL
One Time Event
Math 125

Qualifying Exams  Differential Equations

Math 125
Tue 8 Sep 2015, 1:00pm4:00pm
Details
For more info, please visit http://www.math.ubc.ca/Grad/QualifyingExams/index.shtml
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Tue 8 Sep 2015, 4:30pm
SPECIAL
One Time Event
Math 125

Department Graduate Orientation

Math 125
Tue 8 Sep 2015, 4:30pm6:00pm
Details
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University of Warwick

Thu 10 Sep 2015, 3:30pm
Number Theory Seminar
SFU (room TBA)

TBA

SFU (room TBA)
Thu 10 Sep 2015, 3:30pm4:30pm
Abstract
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Fri 11 Sep 2015, 3:00pm
Department Colloquium

reserved

Fri 11 Sep 2015, 3:00pm4:00pm
Abstract
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University of Alberta

Wed 30 Sep 2015, 3:00pm
Probability Seminar
ESB 2012

The smallest singular value of random matrices with independent entries

ESB 2012
Wed 30 Sep 2015, 3:00pm4:00pm
Abstract
We consider a classical problem of estimating the smallest singular value of random rectangular and square matrices with independent identically distributed entries. The novelty of our results lies in very weak, or nonexisting, moment assumptions on the distribution of the entries. We prove that, given a sufficiently “tall” $N \times n$ rectangular matrix $A = (a_{ij} )$ with i.i.d. entries satisfying the condition $\sup_{\lambda \in \mathbb{R}} \mathbb{P} \left\{ \lvert a_{ij} − \lambda \rvert \le 1 \right\} \le 1/2$, the smallest singular value $s_n (A)$ satisfies $s_n(A) \gtrsim \sqrt{N}$ with probability very close to one.
Our second theorem is an extension of the fundamental result of Bai and Yin from the early 1990’s. Let $\{a_{ij} \}^\infty_{i,j=1}$ be an infinite double array of i.i.d. random variables with zero mean and unit variance, and let $(N_m )_{m=1}^\infty$ be an integer sequence satisfying $\lim_{m \to \infty} \frac{N_m}{m} = r\) for some \(r \in (1, \infty)$. Then, denoting by $A_m$ the $N_m \times m$ topleft corner of the array $\{a_{ij}\}$, we have
\[ \lim_{m \to \infty} \frac{s_m(A_m)}{\sqrt{N_m}} = \sqrt{r}1 \hspace{3mm}\mbox{ almost surely}.\]
This result does not require boundedness of any moments of $a_{ij}$'s higher than the 2nd and resolves a long standing question regarding the weakest moment assumptions on the distribution of the entries sufficient for the convergence to hold.
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Princeton University

Fri 23 Oct 2015, 3:00pm
SPECIAL
Department Colloquium / PIMS Seminars and PDF Colloquiums
ESB2012

TBAPIMS/UBC Distinguished Colloquium

ESB2012
Fri 23 Oct 2015, 3:00pm4:00pm
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Universita di Roma Tor Vergata

Tue 27 Oct 2015, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

TBA

ESB 2012
Tue 27 Oct 2015, 3:30pm4:30pm
Abstract
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Fri 30 Oct 2015, 3:00pm
Department Colloquium

reserved

Fri 30 Oct 2015, 3:00pm4:00pm
Abstract
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Fri 13 Nov 2015, 3:00pm
Department Colloquium

reserved

Fri 13 Nov 2015, 3:00pm4:00pm
Abstract
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UC Berkeley

Fri 4 Mar 2016, 3:00pm
SPECIAL
Department Colloquium
ESB 2012

PIMS Hugh Morris Lecture

ESB 2012
Fri 4 Mar 2016, 3:00pm4:00pm
Abstract
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