16,235 reputation
23664
bio website nd.edu/~lnicolae
location University of Notre Dame
age 50
visits member for 3 years, 4 months
seen 4 hours ago
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
comment Define “Mathematics Colloquium”?
See Lesson 1 in Gian Carlo Rota's 10 lessons alumni.media.mit.edu/~cahn/life/…
Apr
30
comment 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
comment 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
comment 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
comment 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 Non-Linear Analysis, especially Thm. 9.5. vmm.math.uci.edu/PalaisPapers/…
Apr
25
comment random category theory
I do not understand what these categories are because the links you included point to suspicious looking sites.
Apr
25
comment 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
comment 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
comment 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
comment 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
comment 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
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Apr
24
comment 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
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Apr
24
answered First collision time of $n$ random walkers on a cycle
Apr
23
accepted An unusual metric reconstruction problem
Apr
23
comment An unusual metric reconstruction problem
Thanks! That does it.
Apr
23
revised An unusual metric reconstruction problem
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Apr
23
asked An unusual metric reconstruction problem