Math from Krach

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148

📣 Post reach

298

Avg views / post

2×

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🔥 Top post: Let's switch gears. A famous Furstenberg–Sárközy theorem states · 497 views

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🔥 Top post Let's switch gears. A famous Furstenberg–Sárközy theorem states that any square-difference-free set (i.e. set of numbers such that no difference of two numbers from the set is a perfect square) has density zero. The proof is Fourier analysis quite similar… 👁 497

Multiplication table, more than you wanted to know! 👁 386 Let A be a triangle. Suppose points of a circle are coloured in two colours, is it always possible to find a monochromatic triangle similar to A? Turns out, that the answer is yes if and only if A has angles (pi/7, 2pi/7, 4pi/7). More gen… 👁 445 Problem 2: This is a problem from Erdös. Let n_k be a lacunary sequence of positive integers, i.e., n_{k+1} > (1 + \eps)*n_k for some \eps>0. Can we find a real \theta such that all distances from n_k*\theta to the nearest integer are sepa… 👁 363 Looking again at the article about the Lonely Runner Conjecture for 8 runners [2], I noticed that the author also proves an improved version of the statement "if the set of speeds forms a lacunary (enough) sequence then there exists a time… 👁 304 Proceeding further following the transcript we see that Alice, Bob, and Charlie must also identify (x+d, y+d, N-x-y-d) as a YES instance, leading to a contradiction! Now, what can be said about an upper bound for the size of a set avoidi… 👁 253 Here is a surprising neat connection between communication complexity and additive combinatorics. Communication complexity problem: suppose Alice, Bob, and Charlie each have a number written on their hat: a, b, c, all three from 1 to N; … 👁 223 Here is a proof: suppose some stopping time S achieves very small distance to the stationary. Let’s run additional Uniform(1..T) steps on top of S steps. The measure of the end point is still very close to stationary since running a fixed … 👁 205 Here is one interesting fact. When you have a Markov chain (think of a random walk on a finite graph) an important quantity to look at is mixing time: How many steps does one need to take so that the distribution becomes close to the sta… 👁 191 At the end, let me mention that I believe lonely runner conjecture to be wrong with a huge margin. Taking a random time it's easy to see that a gap of 1/(2k) always exists and I believe that for large k, even the bound of 1/(1.99*k) is wro… 👁 268 Anyone interested in improving the state-of-the-art result for the lonely runner conjecture? Lonely runner conjecture states that if k+1 runners start a race running on a circle of unit length with distinct speeds v_1, v_2, ..., v_{k+1} … 👁 260 So, a naive guess for the maximum of \log{\zeta(1/2+i*t)} on a typical interval of length 1 would be to compare it with a maximum of \log{T} random variables, which are independent and each of which has \N(0, 1/2*\log\log T) distribution. … 👁 184

📊 Channel activity & format

Posting cadence

0.38 / week

A lower-frequency channel — each post lands with more weight.

💡 Facts

👁️Averages 298 views per post.

🛡️ Audience credibility

63/100 Good

Est. 81% real, active audience · Low fake-follower risk.
Strong engagement (~2× of followers engage each post) — an active, real audience.

Est. authentic audience

81%

Fake-follower risk

Low

Data confidence

Low

Low confidence — few signals are public for this listing, so treat it as a rough screen. Heuristic estimate from engagement, follower ratios, account age & growth — a screening signal, not a guarantee.

About

Hey, I’m Dmitry Krachun (@dmitrykrachun), currently a postdoc at Princeton, department of mathematics. I mostly post about research level maths that I stumble upon.

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Math from Krach

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