Daniel Shankman

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I am a fourth year graduate student at Purdue University.  My advisor is Freydoon Shahidi.


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Mathematical Interests:

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<li> Algebraic number theory  </li>

<li> Algebraic geometry  </li>

<li> Representation theory </li>

<li> Bruhat-Tits building theory

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My general area of interest is the Langlands Program, a body of work encompassing many areas of mathematics, following <br> a series of influential conjectures by Robert Langlands.  My advisor invented something called local coefficients in the 80s, <br>based off of an idea of Langlands.  
I'm currently working on the problem of the stability of local
coefficients under highly <br>ramified twists.  

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I've been an instructor or taught recitation for the following:

<li> Math 158 (Precalculus and trigonometry) instructor </li>

<li> Math 162 (Calculus II) recitation  </li> 

<li> Math 261 (Calculus III) recitation  </li>

<li> Math 262 (Differential equations and linear algebra) recitation. </li>
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I've graded for the following:

<li> Math 266 (Differential equations) </li>

<li> Math 351 (Linear algebra) </li>

<li> Math 546 (Functional analysis) </li>
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Support: Since Spring 2016, I have been supported by a research assistantship from Dr. Shahidi. <br>

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Notes:


<li> <a href = "https://www.math.purdue.edu/people/bio?user=shahidi&page=Notes+on+Class+Field+Theory.pdf">Class field theory</a>: Notes typed by me and Dongming She based on Dr. Shahidi's Math 684 course. </li>
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Honors and awards:


<li> 2015 Maclane Award.  </li>

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Qualifying exams: I completed  my qualifying exams in August 2015.  
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Here are the exams I took.

<li> August 2014: Abstract algebra (failed, miserably) </li>
<li> January 2015: Real analysis, abstract algebra, topology </li>
<li> August 2015: Complex analysis </li>

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Advanced topics: This is an oral exam based on subjects of your advisor's choosing.
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My advanced topics exam was on class field theory and linear algebraic groups.

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I took the advanced topics exam in August 2016.

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