None, he's an open book.
A highly intelligent bookworm at heart, it's rare to spot Luke with his eyes looking at anything else other than a book's many pages. This borderline unhealthy investment on his hobby has contributed to a shy and quiet guy whom goes under the radar for many people. His unassuming behavior has made it so he never really ruffled anyone's feathers, and in exchange he's been left alone outside of his friends group, never running into much bullying at all throughout his life.
Of course, things are flipped on their head when he opens his mouth. Always the eloquent and charismatic talker, Luke has a way with words and cadence unlike most of his peers, especially for someone like him. His ability to catch other people's attention with his speech is part of what led him to pursue teaching to begin with - not only could he relate to a lot of students in his personality's general awkwardness, but he could make them listen. It's not uncommon for his circle to include people younger than himself because of it.
He's enamored with all sorts of sciences, finding himself to be a jack of all trades when it comes to them, sans for one - his first love is Astronomy (unlike what his ex wife would have you believe) and he's devoted to the matter, pursuing to expand his horizons in it daily. His pure love for the subject made him a shoe in for the various teaching positions he's held over the years and it serves for interesting, interactive lectures for the less-than-magical subject; at least it's still magical in his eyes, despite most of the material relying on Muggle knowledge.
Behind the modest veneer lies an ambitious individual. He knows what he wants and knows how to achieve it, and is willing to employ anything to pursue his goals (within reason). He lends this ingenuity to the school's LARP club as well as his life, as if he weren't to think outside of the box, he'd likely never have pursued a tenure in Tallygarunga to begin with.
He's very protective of those in his life, whether it be family, friends, peers or students, being fully prepared to fearlessly perish in their stead if he has to. Even if he may not be the best person to have more emotional and deep conversations with, he always tries to be there for others - if he can't help them with whatever is ailing them, perhaps they can help him gain a better perspective on various matters instead.
Standing at 173 cm, Luke hasn't always been the tallest of individuals among men his age. He's not too self conscious about his height, however, finding that his tendency to get embarrassed easily is far greater a detriment than whatever judgement others may decide to pass on regarding his shortness. He's not particularly muscular, never having been a sporty person, but he does pay some mind to what he eats and as such he manages to maintain a slim build.
He keeps his curly brown locks at a medium length, and is follically gifted enough to accompany that with a proper, albeit short, beard. His dark brown eyes are shielded by glasses when he's reading, but he's not a fan of wearing them and as such he often shirks that responsibility, something which he will likely pay for at some point later in life.
He can be easily slotted into the 'smart casual' dress code wherever he goes. Neutral colors blend well with his unassuming personality, and he's often seen with chinos, dress shirts, cable knit cardigans and blazers. He's a bit of a fan of Oxfords, having more than a couple pairs. Finally, he avoids ties like the plague, having always fumbled at trying to wear them in the past, to the point he's given up.
While Luke does keep a healthy social circle, he's never had a whole lot in the way of friends. Despite his charismatic way of talking he's still quite timid and shy, avoiding situations that would garner him heavy attention outside of a classroom. Though, even if it's a bit difficult to reach the 'friend' threshold with him, he still strives to keep a positive connection with those around him, even if they are just acquaintances.
As far as his actual friends go, while he prefers to keep to himself in general, he certainly doesn't mind including them in his activities on occasion - especially if they're as enthusiastic as he is about them. Whether it be through science or pop culture, there's always plenty to discuss and interact with when it comes to him.
While he keeps in touch with his family, it's exceedingly rare when Luke sees them nowadays. He does keep in touch through phone calls but given his job's responsibilities he finds it difficult to visit them in England. As for his ex-wife, while no longer his family, remains his close friend. Though, much like his parents, nowadays she suffers the same treatment, made more difficult by the fact she's also teaching in Hogwarts and it isn't as tech-friendly as Tallygarunga is.
Luke crushes easy on people whom happen to share his interests. This is usually a double edged blade - not only is he too shy to approach them usually, but it's common for him to be drawn to more quiet types himself precisely because of the nature of potential shared interests. Once over that hurdle, while he sometimes struggles with self confidence, he proves to be a thoughtful significant other whom wants to be actively invested in his partner's life and make them happy.
Of course, he knows what he wants - settle down, marry (again) and have children. Due to this, any who approach him and reveal they aren't that into such goals are cast aside in the romantic sense on the spot, even if he likes them. Given his general demeanor, these splits are often amicable with no hard feelings on either end.
He's not known to have had many enemies - given that he treats people with kindness, even those that would have something against him at first normally find themselves hard-pressed to continue their hatred. He doesn't go out looking to make enemies and tries to solve things should problems arise, not wanting a cloud of negativity to hang over anybody's head.
Luke Remington Carver first entered the world via the union of Judith and Remington Carver Jr., being born in Manchester, England. From an early age he proved to be a very studious child, being the one kid whom had an abnormal interest in all sorts of scientific subjects - animals, plants, space, chemistry, you name it. This contributed to the boy being somewhat closed off from his peers at first due to diving into mountains of books on a daily bases, becoming an information sponge at the expense of his social life and development.
The shy boy was eventually enrolled in Hogwarts. It was there that he met his eventual wife, Elise, once he was sorted to Ravenclaw - that House, teeming with people like him, proved to be a blessing as he soon made a number of friends and managed to prove to be quite the eloquent speaker in general. Unfortunately, with the Second Wizarding War breaking out at the end of that very first year, his parents wisely made the decision to move to France to shield the boy from any harm that may come to him.
He enrolled in Beauxbatons for the remainder of his mandatory academic career. The fact he had to force himself to learn the language so quickly made it so he was highly social in an effort to grasp French properly, even though he frequently sought refuge in solitude. This was when his love for fantasy and science fiction first developed, as such books served as an escape to his suddenly stressful life. Upon graduation, and with the war long over, Luke decided to return to his country to pursue higher education.
He enrolled in the Douxworth Wizarding University, a campus appealing to both British and French - he felt right at home, dominating the two languages at that point. He was reunited with his brief first year crush in that school, and fortunately, things blossomed. A few years later, upon graduation, the pair got married and relocated to France as both had become employed in Beauxbatons to teach their respective subjects.
It seemed like paradise at first, or at least until Elise took a job offer in Hogwarts instead; that put a damper in their marriage, as Luke always wanted to settle down and have kids, a task that would be quite the feat to accomplish when both parents were in separate countries. It didn't help that eventually he took an offer to teach at Durmstrang instead. They saw each other so little at that point that ultimately they agreed upon divorcing. It was amicable, but it made Luke think about where he wanted to teach so to facilitate his need to have a family. This lead the man to set his sights upon Tallygarunga just as he reached his thirties.
Securing a position in the school, he moved to Australia and hasn't looked back since. He fell in love with the small town and has become wholly convinced that's where he wants to spend the rest of his life in. His tenure has lasted nearly half a decade at that point and it's been the most fun he had teaching in his entire career.