Difference between revisions of "New GAGS"

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== Spring 2020 ==
 
 
 
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|rowspan="2" style="background-color:#dddddd"| January 29
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| Colin Crowley
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|- sytle="bottom-margin:5px"
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| <div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:550px; overflow:auto;"><i>
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A good talk
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</i><div class="mw-collapsible-content">
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owing year he won a decisive victory over the French at the Battle of the Nile and remained in the Mediterranean to support the Kingdom of Naples against a French invasion. In 1801 he was dispatched to the Baltic and won another victory, this time over the Danes at the Battle of Copenhagen. He commanded the blockade of the French and Spanish fleets at Toulon and, after their escape, chased them to the West Indies and back but failed to bring them to battle. After a brief return to England he took over the Cádiz blockade in 1805. On 21 October 1805, the Franco-Spanish fleet came out of port, and Nelson's fleet engaged them at the Battle of Trafalgar. The battle became one of Britain's greatest naval victories, but Nelson, aboard HMS Victory, was fatally wounded by a French sharpshooter. His body was brought back to England where he was
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|-
 
|-
| bgcolor="#D0D0D0" width="120" align="center"|'''Date'''
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|- style="vertical-align:top"
| bgcolor="#A6B658" width="350" align="center"|'''Speaker'''
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|rowspan="2" style="background-color:#dddddd"| January 29
 +
| Colin Crowley
 +
|- style="border-width:0px 0px 0px 3px; border-style:solid"
 +
| <div class="mw-collapsible mw-collapsed" data-expandtext="Show abstract" data-collapsetext="Hide abstract" style="width:550px; overflow:auto;"><i>
 +
A good talk
 +
</i><div class="mw-collapsible-content">
 +
owing year he won a decisive victory over the French at the Battle of the Nile and remained in the Mediterranean to support the Kingdom of Naples against a French invasion. In 1801 he was dispatched to the Baltic and won another victory, this time over the Danes at the Battle of Copenhagen. He commanded the blockade of the French and Spanish fleets at Toulon and, after their escape, chased them to the West Indies and back but failed to bring them to battle. After a brief return to England he took over the Cádiz blockade in 1805. On 21 October 1805, the Franco-Spanish fleet came out of port, and Nelson's fleet engaged them at the Battle of Trafalgar. The battle became one of Britain's greatest naval victories, but Nelson, aboard HMS Victory, was fatally wounded by a French sharpshooter. His body was brought back to England where he was
 +
</div></div>
 
|-
 
|-
|| January 29
 
|| Colin Crowley
 
|-
 
| Can it work?
 
|-
 
| bgcolor="#E0E0E0"| February 5
 
| bgcolor="#C6D46E"| Asvin Gothandaraman
 
|-
 
|}
 
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== January 29 ==
 
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Colin Crowley'''
 
|-
 
| bgcolor="#BCD2EE"  align="center" | Title: Lefschetz hyperplane section theorem via Morse theory
 
|-
 
| bgcolor="#BCD2EE"  | Abstract: Morse theory allows you to learn about the topology of a manifold by studying the critical points of a nice function on the manifold. This perspective produces a nice proof of the theorem in the title, which concerns the homology of smooth projective varieties over C. I'll explain what the theorem says, say something about what Morse theory is and why it's related, and then finish with a neat example. I'm aiming to make this understandable to someone who's taken algebraic geometry 1 and topology 1.
 
|}                                                                       
 
</center>
 
 
== February 5 ==
 
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Asvin Gothandaraman '''
 
|-
 
| bgcolor="#BCD2EE"  align="center" | Title: An introduction to unirationality
 
|-
 
| bgcolor="#BCD2EE"  | Abstract: I will introduce the notion of unirationality and show that cubic hypersurfaces are unirational (following Kollar). If time permits, I will also show that unirational varieties are simply connected.
 
|}                                                                       
 
</center>
 
 
== February 12 ==
 
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Qiao He'''
 
|-
 
| bgcolor="#BCD2EE"  align="center" | Title:
 
|-
 
| bgcolor="#BCD2EE"  | Abstract:
 
|}                                                                       
 
</center>
 
 
== February 19 ==
 
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Dima Arinkin'''
 
|-
 
| bgcolor="#BCD2EE"  align="center" | Title: Blowing down, blowing up: surface geometry
 
|-
 
| bgcolor="#BCD2EE"  | Abstract:A big question in algebraic geometry is how much one can change a variety without affecting it `generically'. More precisely, if two varieties are birational, how far can they be from being isomorphic?
 
 
The question is trivial for (smooth projective) curves: they are birational if and only if they are isomorphic. In higher dimension, the
 
situation is much more interesting. The most fundamental operation are the `blowup', which is a kind of alteration of a variety within its birational isomorphism class, and its opposite, the blowdown.
 
 
In my talk, I will introduce blowups and discuss their properties. Then (time permitting) I would like to look deeper at the case
 
of surfaces, where the combination of blowups and intersection theory provides a complete and beautiful picture. (If we do get to this point, I won't assume any knowledge of intersection theory: to an extent, this talk is my excuse to introduce it.)
 
|}                                                                       
 
</center>
 
 
== February 26 ==
 
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{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Connor Simpson'''
 
|-
 
| bgcolor="#BCD2EE"  align="center" | Title: Intro to Toric Varieties
 
|-
 
| bgcolor="#BCD2EE"  | Abstract: A brief introduction to toric varieties: how to build them, formulas for computing topological data, toric blow-ups, and more.
 
|}                                                                       
 
</center>
 
 
== March 4 ==
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Peter Wei'''
 
|-
 
| bgcolor="#BCD2EE"  align="center" | Title: An introduction to Grothendieck-Riemann-Roch Theorem
 
|-
 
| bgcolor="#BCD2EE"  | Abstract: The classical Riemann-Roch theorem tells you about how topological (genus) and analytical (through line bundle) properties on compact Riemann surface (i.e. smooth projective curve) relate to each other. Moreover, this theorem can be generalized to any vector bundles (or coherent sheaves) over any smooth projective varieties. Eventually, Grothendieck “relativized” this theorem as a property of a morphism between two projective varieties. In this talk I will introduce basic notions to formulate this theorem. If time permitting, enough examples will be given appropriately.
 
|}                                                                       
 
</center>
 
 
== March 11 ==
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Caitlyn Booms'''
 
|-
 
| bgcolor="#BCD2EE"  align="center" | Title: Intro to Stanley-Reisner Theory
 
|-
 
| bgcolor="#BCD2EE"  | Abstract: Stanley-Reisner theory gives a dictionary between combinatorial objects (simplicial complexes) and algebraic objects (Stanley-Reisner rings). In this talk, I will introduce the main objects of study in this theory, describe this dictionary with several examples, and discuss how Stanley-Reisner theory can help us investigate algebra-geometric questions.
 
|}                                                                       
 
</center>
 
 
== March 25 ==
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Steven He'''
 
|-
 
| bgcolor="#BCD2EE"  align="center" | Title:
 
|-
 
| bgcolor="#BCD2EE"  | Abstract:
 
|}                                                                       
 
</center>
 
 
== April 1 ==
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Vlad Sotirov'''
 
|-
 
| bgcolor="#BCD2EE"  align="center" | Title:
 
|-
 
| bgcolor="#BCD2EE"  | Abstract:
 
|}                                                                       
 
</center>
 
 
== April 8 ==
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Maya Banks'''
 
|-
 
| bgcolor="#BCD2EE"  align="center" | Title:
 
|-
 
| bgcolor="#BCD2EE"  | Abstract:
 
|}                                                                       
 
</center>
 
 
== April 15 ==
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Alex Hof'''
 
|-
 
| bgcolor="#BCD2EE"  align="center" | Title: Embrace the Singularity: An Introduction to Stratified Morse Theory
 
|-
 
| bgcolor="#BCD2EE"  | Abstract: Early on in the semester, Colin told us a bit about Morse
 
Theory, and how it lets us get a handle on the (classical) topology of
 
smooth complex varieties. As we all know, however, not everything in
 
life goes smoothly, and so too in algebraic geometry. Singular
 
varieties, when given the classical topology, are not manifolds, but
 
they can be described in terms of manifolds by means of something called
 
a Whitney stratification. This allows us to develop a version of Morse
 
Theory that applies to singular spaces (and also, with a bit of work, to
 
smooth spaces that fail to be nice in other ways, like non-compact
 
manifolds!), called Stratified Morse Theory. After going through the
 
appropriate definitions and briefly reviewing the results of classical
 
Morse Theory, we'll discuss the so-called Main Theorem of Stratified
 
Morse Theory and survey some of its consequences.
 
|}                                                                       
 
</center>
 
 
== April 22 ==
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''Ruofan'''
 
|-
 
| bgcolor="#BCD2EE"  align="center" | Title: Birational geometry: existence of rational curves
 
|-
 
| bgcolor="#BCD2EE"  | Abstract: Rational curves on a variety control its birational geometry. It thus is important to determine whether they exist. People didn’t know how to do this systematically, before Mori discovered a deformation lemma which detect their existence, and bound their degree if they exist. I will briefly introduce Mori’s insight.
 
|}                                                                       
 
</center>
 
 
== April 29 ==
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
| bgcolor="#A6B658" align="center" style="font-size:125%" | '''John Cobb'''
 
|-
 
| bgcolor="#BCD2EE"  align="center" | Title:
 
|-
 
| bgcolor="#BCD2EE"  | Abstract:
 
|}                                                                       
 
 
</center>
 
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Latest revision as of 20:30, 21 April 2020

Date Speaker
January 29 Colin Crowley

A good talk

owing year he won a decisive victory over the French at the Battle of the Nile and remained in the Mediterranean to support the Kingdom of Naples against a French invasion. In 1801 he was dispatched to the Baltic and won another victory, this time over the Danes at the Battle of Copenhagen. He commanded the blockade of the French and Spanish fleets at Toulon and, after their escape, chased them to the West Indies and back but failed to bring them to battle. After a brief return to England he took over the Cádiz blockade in 1805. On 21 October 1805, the Franco-Spanish fleet came out of port, and Nelson's fleet engaged them at the Battle of Trafalgar. The battle became one of Britain's greatest naval victories, but Nelson, aboard HMS Victory, was fatally wounded by a French sharpshooter. His body was brought back to England where he was

January 29 Colin Crowley

A good talk

owing year he won a decisive victory over the French at the Battle of the Nile and remained in the Mediterranean to support the Kingdom of Naples against a French invasion. In 1801 he was dispatched to the Baltic and won another victory, this time over the Danes at the Battle of Copenhagen. He commanded the blockade of the French and Spanish fleets at Toulon and, after their escape, chased them to the West Indies and back but failed to bring them to battle. After a brief return to England he took over the Cádiz blockade in 1805. On 21 October 1805, the Franco-Spanish fleet came out of port, and Nelson's fleet engaged them at the Battle of Trafalgar. The battle became one of Britain's greatest naval victories, but Nelson, aboard HMS Victory, was fatally wounded by a French sharpshooter. His body was brought back to England where he was