Background needed to understand modern research in Algebraic Topology

I am a student of mathematics, and have some background in Algebraic Topology (Hatcher, Bott-Tu, Milnor-Stasheff), Differential Geometry (Lee, Kobayashi-Nomizu), Riemannian Geometry (Do Carmo), and Differential Topology (Hirsch, Minor (Morse Theory), Milnor (h-cobordism theorem)). I would like to learn Floer homology and Khovanov homology.

Q1. Is my background sufficient to learn these topics right now? What are the standard first-level and second-level sources for these topics?

Q2. At the research level, will I need to know any Algebraic Geometry to work in these areas? To give you an idea of my present knowledge, I currently know no algebraic geometry, and even my commutative algebra background has several gaps, especially in parts about DVRs.

Q3. Once I finish books recommended in Q1, what are some good papers to start reading on these areas?

I would greatly appreciate reasoning behind any comments that aren’t strictly factual and are opinions of the writer.

Thank you in advance! 🙂

Is it possible to get SharePoint Online usage metrics for one modern page?

I know SharePoint Online has usage metrics about the whole site but, is it possible to get some more granularity for each page? I mean, is it possible to get the people that visited the home page or a news page that has been created? I would like to have dates, users (anonymous and logged in people), active time, etc.

CSS to change font family in modern communication site

I have a requirement to change the font family in SharePoint modern communication site. I have found a following extension: https://github.com/SharePoint/sp-dev-fx-extensions/tree/master/samples/react-application-injectcss which can be used to inject css.

Question is, what css class do i need to use to change the font throughout the site? Can someone please help, thanks in advance.

Customize Filter Icon and filter pane in a Modern Experience document library

I am learning that the modern experience of SharePoint Online does not leave much room for customization. I had a request from the line of business to make the filter ICON considerably more visible for some of their novice users. I know with the modern experience within a document library the default location is to the right of library designated by the filter icon. I was ask to make it more obvious and basically boldly in the users face when a user opens the library. I have been looking for a setting that would allow me to make such a customization to no avail. Does anyone know of a way to do this if at all using the Modern Experience?

Remove or hide search box from SharePoint Online Modern experience communication HUB

I am rebuilding a SharePoint online site using the Modern Experience and I have started building it out with a communication HUB as the parent site to leverage Mega Menus. The company requirement is to remove OR hide the search box that appears on top the communication HUB page by default. How can I do this as I have found no documentation on the Microsoft Community Sites and elsewhere. enter image description here

What is a good Modern Fantasy investigative system? [on hold]

Specifically, I want to make a modern campaign that will start out this mystery case of the session RPG, and then slowly delve into more and more overt supernatural weirdness. This needs a system that supports a modern campaign setting and fantasy elements. At the moment I have as options USR and GURPS, but USR would require creating whole swaths of rules do deal with some of the stuff and GURPS has a rather steep learning curve. Are there any systems out there that would lend itself to what I want to do?

I want to start them out as detectives. The cases will start mundane enough, but I want to add more and more overt supernatural components to their cases until they are drawn into this hidden world of magic and weirdness hidden from most people. I’d prefer classless as it would give them the flexibility to start learning and incorporating what they discover into their characters.

I’d prefer time consuming, difficult to perform magic over the D&Desque ‘blow things up with a wave of the hand’

I’d probably stick to basically human enemies for much of it, perhaps branching off into some things like ghosts and the like.

As this has been put on hold again, let me just list my critera.

  • Supports a modern day setting (As in 21st century, not 1920’s/30’s) with fantastical elements
  • Works with a custom setting
  • Magic in system should be difficult/time consuming to perform
  • Classless
  • Investigations/Mysteries take priority over combat
  • Private Investigators, not military
  • Ideally the supernatural parts can be hidden until they start cropping up.
  • Enemies mostly human, but some other things can crop up from time to time. It’d be best if the game has pre-made NPC stats, to help save me a bit of work.
  • It must be playable on Roll20 with a group of 4-8 players in a session
  • Online character sheets

Sort of an X-Files/Cthulhu/Haven type thing.

The group in question is mostly accustomed to D&D 3.5. We are a group that meets online, so a character sheet being either in Myth Weavers or there being a google sheets template out there would be helpful, but not required. I don’t care whether or not the system uses miniatures. I don’t have a definite length set for the campaign.

Can we define a single immutant state of a device (modern computer at least) to derive a key from?

Please be open and bear with me, I read a lot about encryption, but practiced very little.

I want to write a simple application that uses common encryption algorithms, but based on a derived key without the users choice. I know this has many drawbacks, but this is out of experiment. I will point what is the most clear drawback later on.

For this, the only practical option that appears to me, is to derive the key with a deterministic function from im-mutant information (hardware state including ROM), like bios serial number for example; But also from other information if possible and with other hidden choices, to add some kind of salt, that is hard to reproduce.

Why is this ? Because it would be practical for easier encryption, if it happens that data use is only relevant to that particular state. If state changes, encrypted state is lost.

At the other hand, the main drawback, probably the first aim of encryption is to hide communicated date through network. This is not our case.

If this is possible, what are possible flaws ?

Using Modern Standard Arabic in Arabic-speaking countries

There are a lot of Arabic-speaking countries each with its own variety of an Arabic dialect with a Modern Standard Arabic (MSA or “Fusha”) being the language of the media and official speech, and Classical Arabic being the language of the Quran.

Would I be understood and is it normal to speak Modern Standard Arabic in the Arabic-speaking countries or do I need to study the dialect of the country where I am traveling to? Is the situation different for North African countries vs countries of the Gulf?

Updating custom columns on Modern Pages with SPFx WebPart vs. PowerApp

I created a Communications Site and under Pages, I added custom columns. Besides letting my authors create the pages, I need a way for my authors to capture this additional information.

Out of the box, the Page Properties gives me a nice “form” that will allow my authors to enter this information, however I want to have more control on the look and feel, I want it to be part of the page and not on the side and I need to add custom validations.

Should I do this with a custom SPFx Webpart or is PowerApps an option for this. So far, looks like PowerApps integration is more prominent with Lists, however on Pages, the PowerApp button doesn’t exist. Does that mean PowerApps is not a good candidate to manipulate data on Pages?

Curious to know what you guys are doing out there.

Thank you