سخنران: -

11 مهر 1403
تا


IRCHEP 1403
Iranian Conference on High Energy Physics
Deciphering the Universe Ciphers
School of Physics, IPM
September 30th-October 2nd, 2024 (9-11 Mehr,1403)

Link: https://physics.ipm.ac.ir/conferences/irchep1403/index.jsp

سخنران: پروفسور آندره کاتایف - موسسه تحقیقات هسته ای آکادمی علوم روسیه - مسکو

11 مهر 1403
11:00 تا 12:00

ساختار ریز سری‌های نظریه اغتشاشی بی‌جرم در کرومودینامیک کوانتومی و تعمیم های رابطه کروتر



Link: https://www.skyroom.online/ch/ipm-particles/seminar

سخنران: بهروز طایفه رضایی, پژوهشگاه دانش‌های بنیادی

11 مهر 1403
14:00 تا 15:00

‎A signed graph is a pair $G_{\sigma}=(G‎, \sigma)$‎, ‎where $G$ is a simple graph and $\sigma$‎, ‎called the signature‎, ‎is a function which assigns 1 or $-1$ to each edge of $G$‎. ‎We call $\sigma$ as an it orthogonal signature of $G$ if‎ $A(G_{\sigma})^2=D$‎, ‎where $A(G_{\sigma})$ is the signed adjacency matrix of $G_{\sigma}$ and $D$ is the diagonal matrix with vertex degrees on the diagonal‎.
‎We have shown that if $G$‎ has an orthogonal signature‎, ‎then $G$ should be regular‎.


‎Graphs with orthogonal signature were crucial in the proof of sensitivity conjecture by Huang in 2019‎. ‎Hunag used an orthogonal signature of hypercube in his proof‎. Alon and Zheng extended it from hypercubes to Cayley graphs of $\mathbb{Z}^{n}_2$‎. ‎Other researchers had considered signed graphs with just two distinct eigenvalues‎. ‎Note that the signed adjacency matrix of an orthogonal signature‎
‎of a $k$-regular graph has only two distinct eigenvalues which are $\pm \sqrt{k}$‎. ‎We also note the signed adjacency matrix of any signature‎ of a $k$-regular graph has spectral radius in the interval $[ \sqrt{k},k]$‎. ‎So an orthogonal signature has the minimum spectral radius among all signatures of a regular graph‎. Orthogonal signatures have been classified for $3$-regular and 4-regular graphs‎. ‎A partial answer for 5-regular graphs is given by Stanic‎.


‎We will discuss general constructions for graphs with orthogonal‎
‎signature and also the classification of orthogonal signatures of $k$-regular‎
‎graphs for a fixed $k$‎, ‎specially for $k = 5‎, ‎6$‎.
‎This is a joint work with Bojan Mohar and Maxwell Levit‎.





Zoom room information:


https://us06web.zoom.us/j/85237260136?pwd=MFSZoKdmRXAjfaSaBzbf19lTaaKglf.1


Meeting ID: 852 3726 0136


Passcode: 362880