bio  website  nd.edu/~lnicolae 

location  University of Notre Dame  
age  50  
visits  member for  3 years, 4 months 
seen  4 hours ago  
stats  profile views  6,381 
I do mostly geometry and topology, with an analytic bias. For the past few years Morse theory has popped up in my research, but not in a conventional way.
1d

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Define “Mathematics Colloquium”?
See Lesson 1 in Gian Carlo Rota's 10 lessons alumni.media.mit.edu/~cahn/life/… 
Apr 30 
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First collision time of $n$ random walkers on a cycle
I am now aware of two arguments proving that for fixed $n$, the expected collision time is quadratic in $k$ as $k\to\infty$. 
Apr 30 
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how wiggly is a generic level set?
You should have a look at Maria Nastasescu images of level sets in her senior thesis. The problem she investigates are closely related to your question. its.caltech.edu/~mnastase/Senior_Thesis.html 
Apr 29 
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First collision time of $n$ random walkers on a cycle
I ran computer simulations in the case of $k=100$ vertices and $n\in\{3,4\}$. For each choice of $n$ I have run random walks with $4000$ randomly chosen initial choices of $n$ vertices. The average collision times I got were $499$, when $n=3$, and $218$, when $n=4$. I have run these simulations twice and the results were within $10$ of the above numbers. 
Apr 28 
revised 
First collision time of $n$ random walkers on a cycle
added 4 characters in body 
Apr 27 
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Sobolev multiplication $\otimes$ of $H^1=W^{1,2}$ in vector bundles
General multiplications results can be found in R.Palais' book Foundations of Global NonLinear Analysis, especially Thm. 9.5. vmm.math.uci.edu/PalaisPapers/… 
Apr 25 
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random category theory
I do not understand what these categories are because the links you included point to suspicious looking sites. 
Apr 25 
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random category theory
Could you give a hint on how you hope to use a concept such a random category theory in understanding the evolution of human language? 
Apr 25 
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Which classes of geometric results or problems can not be achieved by algebraic methods
@Stefan Kohl To my mind $\mathbb{R}$ whatever its definition ought to satisfy a completness condition. Once you allow this concept into the mix, then, to my mind, you have invited analysis into your house. 
Apr 24 
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Which classes of geometric results or problems can not be achieved by algebraic methods
@Stefan Kohl I define $\mathbb{C}$ as the result of adjoining $\sqrt{1}$ to $\mathbb{R}$. 
Apr 24 
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Which classes of geometric results or problems can not be achieved by algebraic methods
@seeker The algebraic proofs in the wikipedia page use some analytic facts such as the existence of a square root of a positive number or the intermediate value theorem. 
Apr 24 
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Which classes of geometric results or problems can not be achieved by algebraic methods
The fundamental theorem of algebra does not have a purely algebraic proof. 
Apr 24 
revised 
First collision time of $n$ random walkers on a cycle
added 25 characters in body 
Apr 24 
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First collision time of $n$ random walkers on a cycle
You're right. I'll change the notation. 
Apr 24 
revised 
First collision time of $n$ random walkers on a cycle
added 13 characters in body 
Apr 24 
answered  First collision time of $n$ random walkers on a cycle 
Apr 23 
accepted  An unusual metric reconstruction problem 
Apr 23 
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An unusual metric reconstruction problem
Thanks! That does it. 
Apr 23 
revised 
An unusual metric reconstruction problem
deleted 9 characters in body 
Apr 23 
asked  An unusual metric reconstruction problem 