Related papers: Monstrous Moonshine over Z?
Cosmic strings are predicted by many field-theory models, and may have been formed at a symmetry-breaking transition early in the history of the universe, such as that associated with grand unification. They could have important…
We give new proofs on Arnold Chord Conjecture and Weinstein Conjecture in M\times C which generalizes the previous works.
No more salient issue exists in contemporary astrophysics and cosmology than that of the elusive "dark matter". For many years already Milgrom's paradigm of modified Newtonian dynamics (MOND) has provided an alternative way to interpret…
We generalize the "miraculous cancellation" formulas of Alvarez-Gaum\'e, Witten and Kefeng Liu to a twisted version where an extra complex line bundle is involved. We also apply our result to discuss intrinsic relations between the higher…
Many past attempts to kill MOND have only strengthened the theory. Better data on galaxy velocity curves clearly favor MOND (without fine-tuning) over cold dark matter. The usual critism on the incompleteness of classical MOND has spurred a…
Important results achieved over the last years on supernova remnants, planetary nebulae and superbubbles are briefly reviewed in the context of X-ray observations. I intend to review the important open scientific questions in these fields,…
Numerous astrophysical observations have shown that classical Newtonian dynamics fails on galactic scales and beyond, if only visible matter is taken into account. The two most popular theoretical concepts dealing with this problem are Dark…
Milgrom has proposed that the appearance of discrepancies between the Newtonian dynamical mass and the directly observable mass in astronomical systems could be due to a breakdown of Newtonian dynamics in the limit of low accelerations…
In this paper we survey the history of, and recent developments on, two major conjectures originating in Zilber's model-theoretic work on complex exponentiation -- Existential Closedness and Zilber-Pink. The main focus is on the modular…
In this work, we establish modular parameterizations for two general formulas for $\frac{1}{\pi}$ that subsume conjectural Ramanujan type formulas due to Z.-W. Sun, which have remained open since 2011. As an application of this, in a…
The (Strong) Slope Conjecture relates the degree of the colored Jones polynomial of a knot to certain essential surfaces in the knot complement. We verify the Slope Conjecture and the Strong Slope Conjecture for 3-string Montesinos knots…
There are many hot discussions in the literature about two competing paradigms in galactic and extra-galactic astronomy and cosmology, namely the Dark Matter and the Modified Newtonian Dynamics (MOND). It is very difficult to challenge MOND…
Brand, Nanongkai, and Saranurak introduced a conjecture known as the Hinted Mv Conjecture. Although it was originally formulated for the matrix case, we generalize it here to the tensor setting.
Modified Newtonian dynamics (MOND) is an alternative theory of gravity that aims to explain large-scale dynamics without recourse to any form of dark matter. However the theory is incomplete, lacking a relativistic counterpart, and so makes…
This talk was given at the Tunguska-2001 international conference but it is not about the Tunguska event. Instead we tried to give some flavor of mirror matter, which is predicted to exist if parity is an unbroken symmetry of nature, to…
We study the shifted convolution sums associated to completely multiplicative functions taking values in $\{\pm 1\}$ and give combinatorical proofs of two recent results in the direction of Chowla's conjecture. We also determine the…
Recent work reported the discovery of a gamma-ray burst (GRB) associated with the galaxy GN-z11 at $z\sim 11$. The extreme improbability of the transient source being a GRB in the very early Universe requires robust elimination of all…
Here we prove some conjectures on the monotony of combinatorial sequences from the recent preprint of Zhi--Wei Sun.
This work develops some technology for accessing the loop expansion of the Kontsevich integral of a knot. The setting is an application of the LMO invariant to certain surgery presentations of knots by framed links in the solid torus. A…
In this note, we describe the parity of the coefficients of the McKay-Thompson series of Mathieu moonshine. As an application, we prove a conjecture of Cheng, Duncan and Harvey stated in connection with Umbral moonshine for the case of…