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 Events
Tue 8 Sep 2015, 9:00am SPECIAL
One Time Event
Math 125
Qualifying Exams - Analysis
Math 125
Tue 8 Sep 2015, 9:00am-12:00pm

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, 1:00pm-4:00pm

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, 1:00pm-4:00pm

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, 4:30pm-6:00pm

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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, 3:30pm-4:30pm

Abstract

 
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Fri 11 Sep 2015, 3:00pm
Department Colloquium
reserved
Fri 11 Sep 2015, 3:00pm-4:00pm

Abstract


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Konstantin Tikhomirov
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, 3:00pm-4:00pm

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 $N_m \times m$ top-left 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 2-nd 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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Yakov Sinai
Princeton University
Fri 23 Oct 2015, 3:00pm SPECIAL
Department Colloquium / PIMS Seminars and PDF Colloquiums
ESB2012
TBA-PIMS/UBC Distinguished Colloquium
ESB2012
Fri 23 Oct 2015, 3:00pm-4:00pm
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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, 3:30pm-4:30pm

Abstract

 
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Fri 30 Oct 2015, 3:00pm
Department Colloquium
reserved
Fri 30 Oct 2015, 3:00pm-4:00pm

Abstract


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Fri 13 Nov 2015, 3:00pm
Department Colloquium
reserved
Fri 13 Nov 2015, 3:00pm-4:00pm

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, 3:00pm-4:00pm

Abstract


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